Question

Show that if X and Y are independent rv’s, then E(XY) 5 E(X) ? E(Y). Then apply this in Exercise 25. [Hint: Consider the continuous case with f (x, y) 5 fX(x) ? fY(y).]

Name: show that if x and y are independent rvs then exy 5 ex ey then apply this in exercise 25 hint consider the continuous case with f x y 5 fxx fyy 53181
Uploaded: 2023-12-29T23:54:29-08:00
Duration: 2 min 1 s
Channel: Ivan Kochetkov
Description: show that if x and y are independent rvs then exy 5 ex ey then apply this in exercise 25 hint consider the continuous case with f x y 5 fxx fyy 53181

          Show that if X and Y are independent rv’s, then E(XY) 5 E(X) ? E(Y). Then apply this in Exercise 25. [Hint: Consider the continuous case with f (x, y) 5 fX(x) ? fY(y).]

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

12/29/2023

Step 1

** Two random variables \(X\) and \(Y\) are independent if the joint probability density function (pdf) can be expressed as the product of their individual pdfs. That is, for continuous random variables, we have: \[ f_{X,Y}(x,y) = f_X(x) \cdot f_Y(y) \] Show more…

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Show that if X and Y are independent rv’s, then E(XY) 5 E(X) ? E(Y). Then apply this in Exercise 25. [Hint: Consider the continuous case with f (x, y) 5 fX(x) ? fY(y).]