Question

Suppose X,Y are discrete random variables, each taking only two distinct values. Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be aware that you have to prove E(XY) =E(X)E(Y) -> X,Y independent and NOT the converse)

          Suppose X,Y are discrete random variables, each taking only two
distinct values.
Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be aware
that you have to prove E(XY) =E(X)E(Y) -> X,Y independent and
NOT the converse)

Added by Christina B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert H M

02/12/2023

Step 1

Since \(X\) and \(Y\) are discrete random variables each taking only two distinct values, let \(X\) take values \(x_1\) and \(x_2\), and \(Y\) take values \(y_1\) and \(y_2\). Show more…

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Suppose X,Y are discrete random variables, each taking only two distinct values. Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be aware that you have to prove E(XY) =E(X)E(Y) -> X,Y independent and NOT the converse)