# Question: Find the percentage errors of the approximations of Exercises 8 26

Find 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.

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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. If X1, X2, . . . , Xn are independent random variables having identical Bernoulli distributions with the parameter θ, then is the proportion of successes in n trials, which we denote by Θ. Verify that (a) E(Θ) = θ; ...Find the sampling distributions of Y1 and Yn for random samples of size n from a continuous uniform population with α = 0 and β = 1. With reference to part (b) of Exercise 8.52, find the covariance of Y1 and Yn. What is the probability of each possible sample if (a) A random sample of size n = 4 is to be drawn from a finite population of size N = 12; (b) A random sample of size n = 5 is to be drawn from a finite population of size ...Post your question