Property 10. If X and Y are independent random variables, then E [h (X ). k (Y)] = E [h (X)] E [k (Y)] - (6-28) .. where h(.) is a function of X alone and k(·) is a function of Y alone, provided expectations on both sides exist.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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Prove the property

Property 10. If X and Y are independent random variables, then
E (h (X ). k (Y)] = E [h (X)] E [k (Y)]
- (6-28)
where h(.) is a function of X alone and k(·) is a function of Y alone, provided expectations on
both sides exist.
Transcribed Image Text:Property 10. If X and Y are independent random variables, then E (h (X ). k (Y)] = E [h (X)] E [k (Y)] - (6-28) where h(.) is a function of X alone and k(·) is a function of Y alone, provided expectations on both sides exist.
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