Question: The skewness of a random variable was defined in Definition 4.4.1. Suppose that X1, . . . , Xn form a random sample from a

The skewness of a random variable was defined in Definition 4.4.1. Suppose that X1, . . . , Xn form a random sample from a distribution F. The sample skewness is defined as

One might use M3 as an estimator of the skewness Î¸ of the distribution F. The bootstrap can be used to estimate the bias and standard deviation of the sample skewness as an estimator of Î¸.
a. Prove thatM3 is the skewness of the sample distribution Fn.
b. Use the 1970 fish price data in Table 11.6 on page 707. Compute the sample skewness, and then simulate 1000 bootstrap samples. Use the bootstrap samples to estimate the bias and standard deviation of the sample skewness.

-X 3/2 ,- M3 =

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