Answered: 1. For any random variable X for which…

1. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]² = E [X(X – 1)] + [E(X)]²

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 40E

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1. For any random variable X for which E(X) and E(X²) are finite, show that
Var(X) = E(X²) – [E(X)]² = E [X(X – 1)] + [E(X)]²

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