Independent trials, resulting in one of the outcomes 1, 2, 3 with respective probabilities p1, p2...

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Independent trials, resulting in one of the outcomes 1, 2, 3 with respective probabilities p1, p2 p3. Ei=1 Pi =1, are performed. (a) Let N denote the number of trials needed until the initial outcome has occurred exactly 3 times. For instance, if the trial results are 3, 2, 1, 2, 3, 2, 3 then N = 7. Find E[N]. (b) Find the expected number of trials needed until both outcome 1 and outcome 2 have occurred. Independent trials, resulting in one of the outcomes 1, 2, 3 with respective probabilities p1, p2 p3. Ei=1 Pi =1, are performed. (a) Let N denote the number of trials needed until the initial outcome has occurred exactly 3 times. For instance, if the trial results are 3, 2, 1, 2, 3, 2, 3 then N = 7. Find E[N]. (b) Find the expected number of trials needed until both outcome 1 and outcome 2 have occurred.

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