1. [0/1.25 Points] DETAILS PREVIOUS ANSWERS UHSTAT4 8.E.020. MY NOTES ASK YOUR TEACHER Consider three tosses of a fair coin. (a) Find the probability distribution function for X = number of tails. k 0 3 P( X = K) I (b) Find the probability distribution function for Y = the difference between the number of heads and the number of tails. k -3 -1 1 3 P( Y = k) (c) Find the probability distribution function for Z = the sum of the number of heads and the number of tails. K 0 1 2 3 P(Z = k)2. [-I1 .25 Points] boy is .5 for each birth. P(B) = P(GB) = P(GGB) = P(GGGB) = passes) = UHSTAT4 8.E.021. (b) Find the probability distribution function for X. k 1 2 P(X = k) ASK YOUR TEACHER PRACTICE ANOTHER A woman decides to have children until she has her rst boy or until she has four children, whichever comes rst. Let X = number of children she has. For simplicity, assume that the probability of a (a) The simple events in the simple space are {B, GB, GGB, GGGB, GGGG}, where we use B for boy and G for girl. For instance, one simple event is GB, because the woman quits once she has a boy. Find the probability for each of the simple events in the sample space. 3. [-/1.25 Points] DETAILS UHSTAT4 8.E.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The probability that Mary will win a game is 0.02, so the probability that she will not win is 0.98. If Mary wins, she will be given $40; if she loses, she must pay $4. IfX = amount of money Mary wins (or loses), what is the expected value ofX? (Round your answer to the nearest cent.) $ 4. [-/1.25 Points] DETAILS UHSTAT4 8.E.037. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER An insurance company expects 15% of its policyholders to collect claims of $700 this year and the remaining 85% to collect no claims. What is the expected value, u, for the amount they will pay out in claims per person? u = $ per person (in the long run)