Suppose a slightly inebriated party-goer returns to his apart- ment in the early hours of the morning. He has three similar keys, just one of which opens his apartment door. He tries one key at a time, selecting keys at random and with replacement. If he makes 4 unsuccessful tries he gives up and knocks on the door until his roommate lets him in. Let X be the number of tries until he succeeds or gives up. Find the probability distribution for X. Then nd E (X) and SD(X) The possible values of X are 1,2,3,4. For the values 1,2,3, the distribution of X is geometric with probability of success equal to 1/3. For example, P(X = 3) = (2/3)2(1/3), that is, the probability of two failures and then a success. Find P(X = 1), P(X = 2), P(X = 4). Make a table to calculate E(X) = 2L1 spur = k) and 130(2) = 23:1 k2P{X = k). Use the formulas Var(X) = E(X2) (E(X))2 and SD(X) = 1fVar{X)