Let X and Y be random variables describing independent tosses of a fair coin. Let Z be the random variable that equals 1 if both X and Y land heads and that equals 0 otherwise.
How many of the following statements are true?
- The collection of random variables {X,Y} is independent.
- The collection of random variables {X,Z} is independent.
- The collection of random variables {Y,Z} is independent.
- The collection of random variables {X,Y,Z} is independent.