Arandom variable with geometric distribution is a discrete variable that can attain values of 1, 2, . . it is used to model the number of trials of a bernoulli (binary) test until the first success occurs. so, if a bernoulli trial can have "success" with probability p and "failure" with probability 1 − p, then the number of iid trials before a success happens follows the geometric distribution. the pmf for this distribution is given by f(k) = (1 − p) k−1p because if the first success is seen at the kth trial, it means that we have seen k − 1 failures in a row and then saw success in the kth trial. 3 33: : 487, spring 2018 homework 1 due date: 9/26/18 at 11: 50pm 4a) someone gives you a coin and tells you it may be a fake coin. furthermore, a fair coin has a 50% probability of heads, while a fake one has only a 20% chance of heads turning up. you toss the coin 3 times in a row, and it turns up tails, and only on the fourth toss, you see the first heads. based on this observation, would you call this coin fair or fake? justify your answer. 4b) suppose we have two scenarios: the probability of success is p1, or probability of success is p2. given values of 0 ≤ p1 < p2 ≤ 1, what is the minimum number of times failures should occur before the first success in order for you to select scenario 1 over scenario 2?