Consider a fair coin that has 0 on one side and 1 on the other side. We flip this coin, independently, twice. Define the following random variables:
X = the result of the first coin flip
Y = the sum of the results of the two coin flips
Z = X*Y
- Determine the distribution functions of X,Y and Z.
- Are X and Y independent random variables?
- Are X and Z independent random variables?
- Are Z and Y independent random variables?
I understand that to be independent random variables they must satisfy the equation P(X=x,Y=y) = P(X=x)P(Y=y) but I am not sure how to show what P(X=x,Y=y) is or similarly what P(X=x,Z=z) and P(Y=y,Z=z) is in this case. Any help would be great.