Given a fair coin and a fair 4 sided die, Jonathan and Joseph run the following experiment. Theyroll the die (letYcorrespond to the random variable associated with the roll). If they roll aytheythe flip the coinynumber of times, letZcorrespond to the random variable associated with thetotal number of heads they flip.(i) Find the marginal PMFs ofYandZ(i. e. findPY(y) andPZ(z)).(ii) Find the conditional PMFs ofYandZ(i. e. findPY|Z(y|z) andPZ|Y(z|y))

Trish receives $450 on the first of each month. josh receives $450 on the last day of each month. both trish and josh will receive payments for next four years. at a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?

Which statement explains how you could use coordinate geometry to prove the opposite sides of a quadrilateral are congruent? a. use the slope formula to prove the slopes of the opposite sides are the same. b. use the slope formula to prove the slopes of the opposite sides are opposite reciprocals. c. use the distance formula to prove the lengths of the opposite sides are the same. d. use the distance formula to prove the midpoints of the opposite sides are the same.

Aof 12 , we to a of 4 to on a .of 4 be ?