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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n"
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"code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n"
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"output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n"
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"text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly"
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"text": " decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n"
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"code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n"
}
},
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"output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n"
}
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"text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n"
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"code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n"
}
},
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"output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n"
}
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{
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"text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n"
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"code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n"
}
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"output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n"
}
},
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"text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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"text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores."
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Checked other resources
Example Code
AIMessageof shape:[ { "lc": 1, "type": "constructor", "id": [ "langchain_core", "messages", "AIMessage" ], "kwargs": { "lc_serializable": true, "lc_kwargs": { "lc_serializable": true, "lc_kwargs": { "lc_serializable": true, "lc_kwargs": { "content": [ { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n" }, { "type": "executableCode", "executableCode": { "language": "PYTHON", "code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n" } }, { "type": "codeExecutionResult", "codeExecutionResult": { "outcome": "OUTCOME_OK", "output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n" } }, { "type": "text", "text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly" }, { "type": "text", "text": " decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." } ], "additional_kwargs": { "originalTextContentBlock": { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." }, "finishReason": "STOP" }, "response_metadata": { "model_provider": "google", "finishReason": "STOP" }, "tool_call_chunks": [], "tool_calls": [], "id": "run-019d4675-24e3-7642-a838-591cbe623ac7", "usage_metadata": { "input_tokens": 184, "output_tokens": 717, "total_tokens": 1895, "input_token_details": { "text": 184, "cache_read": 0 }, "output_token_details": { "reasoning": 328 } }, "invalid_tool_calls": [] }, "lc_namespace": [ "langchain_core", "messages" ], "id": "run-019d4675-24e3-7642-a838-591cbe623ac7", "content": [ { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n" }, { "type": "executableCode", "executableCode": { "language": "PYTHON", "code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n" } }, { "type": "codeExecutionResult", "codeExecutionResult": { "outcome": "OUTCOME_OK", "output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n" } }, { "type": "text", "text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." } ], "additional_kwargs": { "originalTextContentBlock": { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." }, "finishReason": "STOP" }, "response_metadata": { "model_provider": "google", "finishReason": "STOP" }, "type": "ai", "tool_calls": [], "invalid_tool_calls": [], "tool_call_chunks": [], "usage_metadata": { "input_tokens": 184, "output_tokens": 717, "total_tokens": 1895, "input_token_details": { "text": 184, "cache_read": 0 }, "output_token_details": { "reasoning": 328 } } }, "lc_namespace": [ "langchain_core", "messages" ], "id": "run-019d4675-24e3-7642-a838-591cbe623ac7", "content": [ { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n" }, { "type": "executableCode", "executableCode": { "language": "PYTHON", "code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n" } }, { "type": "codeExecutionResult", "codeExecutionResult": { "outcome": "OUTCOME_OK", "output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n" } }, { "type": "text", "text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." } ], "additional_kwargs": { "originalTextContentBlock": { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." }, "finishReason": "STOP" }, "response_metadata": { "model_provider": "google", "finishReason": "STOP" }, "type": "ai", "tool_calls": [], "invalid_tool_calls": [], "tool_call_chunks": [], "usage_metadata": { "input_tokens": 184, "output_tokens": 717, "total_tokens": 1895, "input_token_details": { "text": 184, "cache_read": 0 }, "output_token_details": { "reasoning": 328 } } }, "lc_namespace": [ "langchain_core", "messages" ], "id": "run-019d4675-24e3-7642-a838-591cbe623ac7", "content": [ { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n" }, { "type": "executableCode", "executableCode": { "language": "PYTHON", "code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n" } }, { "type": "codeExecutionResult", "codeExecutionResult": { "outcome": "OUTCOME_OK", "output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n" } }, { "type": "text", "text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." } ], "additional_kwargs": { "originalTextContentBlock": { "type": "text", "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\nThese values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." }, "finishReason": "STOP" }, "response_metadata": { "model_provider": "google", "finishReason": "STOP" }, "type": "ai", "tool_calls": [], "invalid_tool_calls": [], "tool_call_chunks": [], "usage_metadata": { "input_tokens": 184, "output_tokens": 717, "total_tokens": 1895, "input_token_details": { "text": 184, "cache_read": 0 }, "output_token_details": { "reasoning": 328 } } } } ]transforms into this
generateContentrequest body:{ "role": "model", "parts": [ { "text": "To render the IQ normal distribution, we need to consider its standard parameters: a mean (μ) of 100 and a standard deviation (σ) of 15.\n\nThe normal distribution for IQ scores describes how these scores are typically spread across a population. Most people will have IQ scores clustering around the mean of 100, with fewer people having very high or very low scores.\n\nHere's how the probability density function (PDF) looks at key points for an IQ distribution:\n\n" }, { "type": "executableCode", "executableCode": { "language": "PYTHON", "code": "import math\n\nmu = 100\nsigma = 15\n\ndef normal_pdf(x, mu, sigma):\n coefficient = 1 / (sigma * math.sqrt(2 * math.pi))\n exponent = -((x - mu)**2) / (2 * sigma**2)\n return coefficient * math.exp(exponent)\n\n# Calculate PDF for some representative IQ scores\niq_scores = [40, 55, 70, 85, 100, 115, 130, 145, 160]\npdf_values = {score: normal_pdf(score, mu, sigma) for score in iq_scores}\n\nfor score, pdf in pdf_values.items():\n print(f\"IQ Score: {score}, PDF Value: {pdf:.6f}\")\n" } }, { "type": "codeExecutionResult", "codeExecutionResult": { "outcome": "OUTCOME_OK", "output": "IQ Score: 40, PDF Value: 0.000009\nIQ Score: 55, PDF Value: 0.000295\nIQ Score: 70, PDF Value: 0.003599\nIQ Score: 85, PDF Value: 0.016131\nIQ Score: 100, PDF Value: 0.026596\nIQ Score: 115, PDF Value: 0.016131\nIQ Score: 130, PDF Value: 0.003599\nIQ Score: 145, PDF Value: 0.000295\nIQ Score: 160, PDF Value: 0.000009\n" } }, { "text": "These values show the characteristic \"bell curve\" shape:\n\n* The highest point of the distribution is at the mean (IQ 100).\n* The curve is symmetrical around the mean.\n* As you move further away from the mean (towards very low or very high IQ scores), the probability density rapidly decreases, indicating fewer individuals at those extreme ends.\n\nThis data could be used to plot the classic bell curve for IQ scores." } ] },Error Message and Stack Trace (if applicable)
which results in an Error from Gemini API:
{ "url": "https://generativelanguage.googleapis.com/v1beta/models/gemini-2.5-flash:streamGenerateContent?alt=sse", "status": 400, "body": { "error": { "code": 400, "message": "Invalid JSON payload received. Unknown name \"type\" at 'contents[1].parts[1]': Cannot find field.\nInvalid JSON payload received. Unknown name \"type\" at 'contents[1].parts[2]': Cannot find field.", "status": "INVALID_ARGUMENT", "details": [ { "@type": "type.googleapis.com/google.rpc.BadRequest", "fieldViolations": [ { "field": "contents[1].parts[1]", "description": "Invalid JSON payload received. Unknown name \"type\" at 'contents[1].parts[1]': Cannot find field." }, { "field": "contents[1].parts[2]", "description": "Invalid JSON payload received. Unknown name \"type\" at 'contents[1].parts[2]': Cannot find field." } ] } ] } } }Description
The
typeproperty isn't stripped from these two google-specific content chunk types.System Info
Package:
@langchain/googleVersion:
0.1.9Companion:
@langchain/core1.1.37(peerDependency enforced)Runtime:
bun1.3.11Platform:
Ubuntu 25.10 (Linux 6.17.0-14-generic)