a) In a randomized controlled experiment, it costs researchers t dollars to study each subject in the treatment group and c dollars to study each subject in the control group. Suppose each of n subjects is randomized into one of the two groups according to whether a p-coin lands heads (treatment) or tails (control). Find the expected total cost to study all n subjects. b) I toss n p-coins. Those that land tails I toss again, and then I stop. Find the expected total number of heads. c) I have one 0.25-coin, one fair coin, and three 0.75-coins. I pick one of the five coins at random and toss it till I get 10 heads. Find the numerical value of the expected number of tosses.