Qm
Statistics

Combined height of two independent people

normalsumsmoments

One person's height is X∼N(mean 70, variance 16)X \sim N(\text{mean } 70,\ \text{variance } 16) inches; an unrelated person's is Y∼N(mean 65, variance 9)Y \sim N(\text{mean } 65,\ \text{variance } 9) inches, independent of XX. Let S=X+YS = X + Y be their combined height.

What are the mean and variance of SS, and what is its distribution?

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Cumulants and the Cumulant Generating FunctionExpectation, Variance & MomentsMethod of Moments and GMMMoment Generating FunctionsSkewness and Kurtosis

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