Complete the following:
The following problem develop the concept of determining the probability distribution of a random variable and its mean and variance.
A fair coin is tossed three times. Describe the sample space Ω.
Let X be random variable that denotes the number of heads on the first toss. Describe the probability frequency distribution of X. Find the mean E(X) and variance Var(X).
Let Y be another random variable that counts the total number of heads. Describe the probability frequency distribution of Y , and evaluate E(Y) and Var(Y ).
Describe the frequency distribution of the ordered pair Z = (X, Y ). Then evaluate E(Z) and Var(Z).
Describe the frequency distribution of the product W = XY . Then evaluate E(W) and Var(W).