37. If X is a random variable having the standard normal distribution and Y = X2, show that cov(X, Y) = 0 even though X and Y are evidently not independent.

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.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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37. If X is a random variable having the standard normal
distribution and Y= X², show that cov(X, Y) = 0 even
though X and Y are evidently not independent.
Transcribed Image Text:37. If X is a random variable having the standard normal distribution and Y= X², show that cov(X, Y) = 0 even though X and Y are evidently not independent.
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