3. A fair die is tossed independently and repeatedly. Let X be the number of tosses needed to turn up the first 3. (a) Find P(X = 1), P(X = 2) and P(X = 3). (b) Find the probability mass function of X. (c) Show that the probability mass function you found in part (b) is a valid probability mass function

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srikarmargamLv2

28 Mar 2023

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Q5. Let (Ω, F , P) be a probability space. Let λ > 0 be some constant.

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amaranthwalrus338

Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X]=1.8, what is (a) the largest possible value of P{X=3}? (b) the smallest possible value of P{X=3}? In both cases, construct a probability scenario that results in P{X=3} having the stated value. Hint: For part (b), you might start by letting U be a uniform random variable on (0, 1) and then defining the trials in terms of the value of U.