Coins and dice. let x be a fair dice roll, that is a sample from the uniform distribution in {1, 2, }. let y be the number of heads in x tosses of a fair coin, that is a coin which is landing heads with probability and tails otherwise. we assume the outcome of each coin toss is independent from the outcome of the other coin tosses and from x. a. compute e (y|x = x) for any x = 1,2, . b. prove that e(y) = e(x) and derive the value of e (y). explain intuitively why (1) makes sense.

Ajar contains a mixture of 20 black marbles, 16 red marbles, and 4 white marbles, all the same size. find the probability of drawing a white or red marble on the first draw. 125 12 01 next question ask for turn it in

The krasnapolski is a top-of-the-line hotel in amsterdam, the netherlands. among their many services, they rent bicycles to guests. the bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. on average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. guests keep bicycles for four days on average, with a standard deviation of two days. how long does a guest on average have to wait for a bike? a. approximately 24 hours b. approximately 0.033 hours c. approximately 4 days d. approximately 47 minutes

Which of the following is not a subset of {1,2,3}?