. You flip a penny 3 times and a dime 2 times. Let Hp be the number of times the penny lands on heads, Hd the number of times the dime lands on heads, and H the total number of heads on the two coins combined. Finally, let the random variable M be the number of times the penny lands on heads multiplied by the number of times the dime lands on heads. In other words: H = Hp + Hd M = Hp × Hd (a) Find the probability distribution of H and the probability distribution of M (b) Find the cumulative probability distributions of H and M (c) Are H and M independent? Justify your answer mathematically. (d) Find E[H2 ] and E[M2 ] (e) Find V ar(H) and V ar(M)