Question: Use the results of Exercises 8 25 and 8 27 to show
Use the results of Exercises 8.25 and 8.27 to show that if X has a chi-square distribution with v degrees of freedom, then for large v the distribution of √2X – √2v can be approximated with the standard normal distribution. Also, use this method of approximation to rework Exercise
Answer to relevant QuestionsFind the percentage errors of the approximations of Exercises 8.26 and 8.28, given that the actual value of the probability (rounded to five decimals) is 0.04596. Verify that if X has an F distribution with v1 and v2 degrees of freedom and v2 → ∞, the distribution of Y = v1X approaches the chi-square distribution with .1 degrees of freedom. Verify the results of Example 8.4, that is, the sampling distributions of Y1, Yn, and X~ shown there for random samples from an exponential population. Duplicate the method used in the proof of Theorem 8.16 to show that the joint density of Y1 and Yn is given by (a) Use this result to find the joint density of Y1 and Yn for random samples of size n from an exponential ...How many different samples of size n = 3 can be drawn from a finite population of size (a) N = 12; (b) N = 20; (c) N = 50?
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