Previous Quiz - Q.4Lecture 5 ExamplesMath 370X - Lecture 5 ExamplesFrequently Used Discrete DistributionsSaumil PadhyaOctober 10, 2016Previous Quiz - Q.4Let X1, X2, X3be a random sample from a discrete distribution with probability functionp(x) =13for x = 023for x = 10 otherwiseDetermine the moment generating function, M(t), of Y =X1+X2+X3whereX1, X2, X3areindependent.(A)1927+827et(B) 1 + 2et(C) (13+23et)3(D)127+827e3t(E)13+23e3t1Lecture 5 ExamplesExample 1:Suppose that X is a discrete random variable that is uniformly distributed on theeven integers x = 0,2,4,. . . ,22 so that the probability function of X is p(x) =112for each eveninteger x from 0 to 22. Find E[X] and Var[X].Example 2:If X is the number of “6”s that turn up when 72 ordinary dice are independentlythrown, find the expected value of X2.Example 3:Assume that the number of hits, X, per baseball game, has a Poisson Distribution.If the probability of a no-hit game is110000, find the probability of having 4 or more hits in aparticular game.Example 4:In tossing a fair die repeatedly (and independently on successive tosses), find theprobability of getting the first “1” on the 5-th toss. Find the expected number of tosses beforethe first “1” is tossed.Example 5:In tossing a fair die repeatedly (and independently on successive tosses), find theprobability of getting the third “1” on the 5-th toss.Example 6:An urn contains 6 blue and 4 red balls. 6 balls are chosen at random and withoutreplacement from the urn. If X is the number of red balls chosen, find the standard deviation
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