4. Andy's party. Andy has invited 12 people to his birthday party on Saturday. However, he only made 10 party favors since he thinks that no more than 10 people will actually show up. Assume that the probability that a guest is a no-show is 0.1 and that they behave independently. (a) (6 points) Let X denote the number of guests that show up for Andy's party. What is the name of the distribution of X and what are the mean (E(X)) and variance (V(X)) of the number of guests who show up? Justify your answer. (b) (5 points) What is the probability that every guest who shows up gets a party favor? (c) (5 points) What is the probability that Andy will have one or more party favors left over?
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The distribution of X: Since each guest has a probability of 0.1 of not showing up and 0.9 of showing up, and they behave independently, the distribution of X is a binomial distribution with parameters n = 12 (number of guests invited) and p = 0.9 (probability of Show more…
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