Let y ∼ exp( β ). Derive m y ( t ), the mgf of y (your answer shall be an explicit function of β and t , and shall not contain any expectation or integration). Why is the mgf undefined for t ≥ 1 β.

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.

Madeline takes her family on a boat ride. going through york canal, she drives 6 miles in 10 minutes. later on as she crosses stover lake, she drives 30 minutes at the same average speed. which statement about the distances is true?

One positive integer is 2 less than another. the product of the two integers is 24. what are the integers?