Suppose that Y is a discrete random variable with mean u and variance ot and let W = 5Y.(a) Do you expect the mean of W to be larger than, smaller than, or equal to µ = E(Y)? Why?O The mean of W will be larger than the mean of Y if u < 0, smaller if u > 0 and equal to u if u = 0.O The mean of W will be larger than the mean of Y if u > 0, smaller if u < 0 and equal to u if u = 0.O The mean of W will be larger than the mean of Y if u = 0, smaller if u < 0 and equal to u if u > 0.O The mean of W will be larger than the mean of Y if u = 0, smaller if u > 0 and equal to u if u < 0.O The mean of W will be larger than the mean of Y if u < 0, smaller if u = 0 and equal to u if u > 0.(b) Use the theorem below to express E(W) = E(5Y) in terms of u, where u = E(Y).Let Y be a discrete random variable with probability function p(v), g(Y) be a function of Y, and c be a constant. Then E[cg(Y)] = cE[g(Y)].E(W) =Does this result agree with your answer to part (a)?O YesO No(c) Recalling that the variance is a measure of spread or dispersion, do you expect the variance of W to be larger than, smaller than, or equal to o? = V(Y)? Why?O The variance of W will be smaller than o, since the spread of values of W has decreased.O The variance of W will be equal to o?, since the spread of values of W has not changed.O The variance of W will be larger than o, since the spread of values of W has decreased.O The variance of W will be larger than o?, since the spread of values of W has increased.O The variance of W will be smaller than o?, since the spread of values of W has increased.

Answered: Image /qna-images/answer/533a040c-a54b-457a-9269-8cd048ff8a72.jpg

Suppose that Y is a discrete random variable with mean u and variance o and let W = 5Y. (a) Do you expect the mean of W to be larger than, smaller than, or equal to µ = E(Y)? Why? O The mean of W will be larger than the mean of Y if u < 0, smaller if u > 0 and equal to u if u = 0. O The mean of W will be larger than the mean of Y if u > 0, smaller if u < 0 and equal to u if u = 0. O The mean of W will be larger than the mean of Y if u = 0, smaller if u < 0 and equal to u if u > 0. O The mean of W will be larger than the mean of Y if u = 0, smaller if u > 0 and equal to u if u < 0. O The mean of W will be larger than the mean of Y if u < 0, smaller if u = 0 and equal to u if u > 0. (b) Use the theorem below to express E(W) = E(5Y) in terms of u, where u = E(Y). Let Y be a discrete random variable with probability function p(y), g(Y) be a function of Y, and c be a constant. Then E[cg(Y)] = cE[g(Y)]. E(W) = Does this result agree with your answer to part (a)? O Yes O No (c) Recalling that the variance is a measure of spread or dispersion, do you expect the variance of W to be larger than, smaller than, or equal to o? = v(Y)? Why? O The variance of W will be smaller than o?, since the spread of values of W has decreased. O The variance of W will be equal to o?, since the spread of values of W has not changed. O The variance of W will be larger than o, since the spread of values of W has decreased. O The variance of W will be larger than o?, since the spread of values of W has increased. O The variance of W will be smaller than o2, since the spread of values of W has increased.

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...