# Paper Writing Services P(X k) P(Y k), for any k. If true, provide a proof. If not true, provide a counterexample. (nt: if you’re having

Abstract
why not? 2. Suppose X is a binomial random variable with parameters n and p. (i.e., there are n trials). Suppose Y is a binomial random variable with parameters n and q. Suppose also that 0 p < q 1. True or false?: P(X k) P(Y k), for any k. If true, provide a proof. If not true,

1. John has a choice between two options, to play 3 tennis sets with s father (”F”) and Bill (”B”), a tennis champion. He can either play in the order F-B-F, or in the order B-F-B. Bill is a better player than s father. If John wins two sets in a row, he will win a prize. (a) Wch order should John choose? Why? (b) Let Z be the number of times John wins. If, instead, John wanted to maximize E[Z], should he make a different choice? Why or why not? 2. Suppose X is a binomial random variable with parameters n and p. (i.e., there are n trials). Suppose Y is a binomial random variable with parameters n and q. Suppose also that 0 p < q 1. True or false?: P(X k) P(Y k), for any k. If true, provide a proof. If not true, provide a counterexample. (nt: if you’re having trouble, simplify by considering small n.)

Sample references
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