# Question: With reference to Exercise 8 2 show that if the two

With reference to Exercise 8.2, show that if the two samples come from normal populations, then 1 – 2 is a random variable having a normal distribution with the mean µ1 – µ2 and the variance σ21/n1 + σ22/n2.

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Use Stirling’s formula of Exercise 1.6 on page 16 to show that when v → ∞, the t distribution approaches the standard normal distribution. Verify that if T has a t distribution with v degrees of freedom, then X = T2 has an F distribution with v1 = 1 and v2 = v degrees of freedom. Find the sampling distribution of the median for random samples of size 2m+ 1 from the population of Exercise 8.46. Use the formula for the joint density of Y1 and Yn shown in Exercise 8.52 and the transformation technique of Section 7.4 to find an expression for the joint density of Y1 and the sample range R = Yn – Y1. If a random sample of size n = 3 is drawn from a finite population of size N = 50, what is the probability that a particular element of the population will be included in the sample?Post your question