Question

The expectation of the product of two independent
variables X and Y is equal to:​

Answer 1

Step 1: Given data

Two variables $X$ and $Y$ are independent variables.

Expectation of product of $X$ and $Y$, $E(XY)=?$

Step 2: Calculating $E(XY)$

We know that covariance of two variables is calculated using formula,

$cov(X,Y)=E(XY)-E(X)E(Y)$

Now, since $X$ and $Y$ are independent variables

$\therefore cov(X,Y)=0$

$0=E(XY)-E(X)E(Y)$

$E(XY)=E(X)E(Y)$

Hence, expectation of $XY$ is equal to the product of the expectation of $X$ and the expectation of $Y$.

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Answer 2

Answer:

The expectation of the product of two independent variables X and Y are equal to the product of expectation of X and expectation of Y.

$E(XY) = E(X)E(Y)$

Step-by-step explanation:

Given in the question -

We have to find the expectation of the product of two numbers $E(XY)$-

As we know -

$Cov(X,Y) = E(X)E(Y) -E(XY)$

As it is given X and Y are independent variables so,

$Cov(X,Y) = 0$

Then,

$E(XY) =E(X)E(Y)$

Hence we got the answer.

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