1. Random Numbers of Trials As in lecture and the textbook, we will use "pcoin" to mean a coin that lands heads with probability p. a) In a randomized controlled experiment, it costs researchers 1 dollars to study each subject in the treatment group and 6 dollars to study each subject in the control group. Suppose each of 11 subjects is randomized into one of the two groups according to whether a 11-min lands heads (treatment) or tails (control). Find the expected total cost to study all n subjects. b) | toss n p-coins. Those that land tails l toss again, and then I stop. Find the expected total number of heads. c) l 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