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If X1 and X2 are several independent random variables with distribution to the given data respectively...

If X1 and X2 are several independent random variables with distribution to the given data respectively by P(Xi = −1) = P (Xi = 1) = 1/2 , for i = 1,2, are X1 and X1X2

are independent? Justify your answer.
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Answer #1

Answer:-

Given that:-

If X1 and X2 are several independent random variables with distribution to the given data respectively by P(Xi = −1) = P (Xi = 1) = 1/2 , for i = 1,2, are X1 and X1X2 are independent? Justify your answer.

Given,

If X1 and X2 are independent random variables with distribution given as

Then,

= 0

= 1

= 0

= 1 x 0

= 0

= 0

= 0 - 0

From Equation (1) we get,

X1 and X2 are independent.

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