Use Stirling’s formula of Exercise 1.6 on page 16 to show that when v → ∞, the t distribution approaches the standard normal distribution.
Answer to relevant QuestionsUse the transformation technique based on Theorem 7.2 on page 218 to rework the proof of Theorem 8.14. Let f = u/v1 v/v2 and w = v.) If X has an F distribution with v1 and v2 degrees of freedom, show that Y = 1/X has an F distribution with v2 and v1 degrees of freedom. Find the mean and the variance of the sampling distribution of Y1 for random samples of size n from the population of Exercise 8.46. Use the result of Exercise 8.54 and that of part (a) of Exercise 8.52 to find the sampling distribution of R for random samples of size n from an exponential population. For random samples from an infinite population, what happens to the standard error of the mean if the sample size is (a) Increased from 30 to 120; (b) Increased from 80 to 180; (c) Decreased from 450 to 50; (d) decreased ...
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