Question

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

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 .

Calculate the covariance of Y1 and Y2 .

Cov(Y1,Y2)=
unanswered

Calculate the variance of Z1 .

Var(Z1)=
unanswered

Calculate the covariance of Z1 and Z2 .
Cov(Z1,Z2)=
unanswered

Answer 1

I got

Cov(Y1,Y2)=1/2
Var(Z1)= 3/16
Cov(Z1,Z2)=0