2. Two coins that look identical (they will be identified in this problem as coin #0 and coin #1) are highly biased. The probability of flipping heads with coin #1 is q = 0.4, and the probability of flipping heads with coin #230 is q = 0.2. One coin is picked up at random (which means that the probability po of picking up coin #0 is the same as the probability p of picking up coin #1. The coin that is picked up is flipped and it is observed the number of flips it takes to observe heads for the first time. So the observation random variable Z is the number of flips it takes to observe heads for the first time. a) Set up the likelihood ratio test to decide based on the observation Z whether coin #1 was picked up (Hypothesis H) and flipped, or coin #0 was picked up (Hypothesis H) and flipped. Hint: the conditional probability density functions that make up the likelihood ratio should be replaced with the conditional PMFs since the observation in this problem is a discrete random variable (as opposed to a continuous random variable)