Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variables

Question

Y1 =X1−X3,
Y2 =X2−X3.
We further introduce indicator random variables Zi∈{0,1} with Zi=1 if and only if Yi=0 for i=1,2 .

1. Calculate the covariance of Y1 and Y2.
(Give an exact answer or a decimal accurate to at least 3 decimal places.)
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2. Calculate the variance of Z1.
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3. Calculate the covariance of Z1 and Z2.
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Answer 1

It's a simple question.

Think in lines of binomial random variables and basic cov formulas