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 |
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,
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