6. In LOTTO 4-0, Michigan's lottery game, a player se- lects 6 integers out of the rst 49 positive integers. The state then randomly selects 6 out of the rst 49 positive integers. Cash prizes are given to a player who matches 4, 5, or 8 integers. Let X eqal the num ber of integers selected by a player that match integer selected by the state. (a) State Determine the pmf of X. (b) Calculate the mean, variance, and standard deviation. 7. According to recent national poll, about 40% of Americans believe in ghosts. Assuming this percent age is accurate, if 20 people were randomly selected and asked if they believed in ghosts, what is the prob ability that at least 12 would say they do