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8.23 Show that the expression for the variance of a random variable can be expressed in terms of the first and second moments as Var(X) = E[X³] - E[X]²

8.23 Show that the expression for the variance of a random variable can be expressed in terms of the first and second moments as Var(X) = E[X³] - E[X]²

Calculus For The Life Sciences
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
Section13.3: Special Probability Density Functions
Problem 30E
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I need help with problem 8.23. Steps of what's going on would be helpful. Please and thank you!

8.23 Show that the expression for the variance of a random variable can be expressed in terms of the first and second moments as Var(X) = E[X²] - E[X]²
Transcribed Image Text:8.23 Show that the expression for the variance of a random variable can be expressed in terms of the first and second moments as Var(X) = E[X²] - E[X]²
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