Consider n independent observations of a random variable Y that has skewness coefficient S = E(Y )3/3. (a)Show how E(Y )3 relates to E(Y )3. Based on this, show that the skewness coefficient for the sampling distribution of Y satisfies skewness of Y = S/n. Explain how this result relates to the Central Limit Theorem. (b) Suppose that we can select a value M such that we regard a distribution having S < M as being "close" to bell-shaped. With simple random sampling, show that the sampling distribution of Y is then approximately normal if n > (S/M)2. (c) Plots of common distributions such as the Poisson and gamma with various values of S suggest that S M 0.32 is reasonable for giving a bell shape. For this M, show that Y has an approximate normal sampling distribution when n 10S2. For this guideline, how large a random sample do you need from an exponential distribution to achieve close to normality for the sampling distribution? (recall that exponential distribution has skewness =2)