Question

A fair coin is tossed twice. Let X and Y be random variables such that:

-X = 1 if the first toss is heads, and X = 0 otherwise.

-Y = 1 if both tosses are heads, and Y = 0 otherwise.

Determine whether or not X and Y are independent.

So far, I have determined the the joint probability distribution as follows:

	x = 0	x = 1
y = 0	2/4	1/4
y = 1	0	1/4

Answer 1

here P(Y=0)= 2/4+1/4 =3/4

and P(X=0)=2/4+0 =2/4=1/2

P(X=0,Y=0)=2/4=1/2

as P(X=0)*P(Y=0)=(3/4)*(1/2)=3/8 is not equal to P(X=0,Y=0) , therefore X and Y are not independent,