Random Vectors with Different Units

Define a joint height‐weight distribution with assumed correlation of 0.65.

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hw\[ScriptCapitalD] = BinormalDistribution[{Quantity[1.8, "Meters"], Quantity[85, "Kilograms"]}, {Quantity[0.15, "Meters"], Quantity[9, "Kilograms"]}, 0.65]

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Compute the probability of a person's height being over 1.75 meters, given that the person's weight is above 72 kilograms.

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NProbability[ h > Quantity[1.75, "m"] \[Conditioned] w > Quantity[72, "kg"], {h, w} \[Distributed] hw\[ScriptCapitalD]]

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Compute the distribution of the body mass index (BMI) for the assumed population.

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bmi\[ScriptCapitalD] = TransformedDistribution[ w/h^2, {h, w} \[Distributed] hw\[ScriptCapitalD]]

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Estimate the distribution of the BMI using a sample histogram.

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sample = RandomVariate[bmi\[ScriptCapitalD], 10^5]; Histogram[sample, Automatic, "PDF", AxesLabel -> Automatic]

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