MATH 1550H Midterm: MATH1550H-Test2-Solutions
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[10 = 2 5 each: a fair standard die is rolled until either 1 or 2 comes up. 1: verify that f (x) = . 0 x 0 x 0 is a valid density function: a fair coin is tossed three times. The random variable u counts how many tails came up in the three tosses and the random variable v counts how many heads came up on the second of the three tosses. Determine whether u and v are independent or not. Each face of a fair standard die has a probability of 1. 6 + 1 given roll, so the probability that a roll will come up with 1 or 2 is 1. Rolling the die until it comes up with 1 or 2 and counting the number of rolls required therefore has a geometric distribution with probability of success p = 1. 3 and of failure of q = 1 p = 2 on each triel.
