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suggested exercises-I

# suggested exercises-I - σ 2 further assume x 1 =-0.75 x 2...

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MATH 260 SUGGESTED EXERCISES 1. Exercise 6.64 in page 356 of the textbook. 2. A large construction firm has won 60% of the jobs for which it has bid. Suppose this firm bids on 36 jobs next month. Approximate the probability that it will win at least 20 of these. Approximate the probability that it will win exactly 20 of these. 3. Exercise 7.4 in page 362 of the textbook. 4. Exercise 7.6 in page 362 of the textbook 5. Suppose that two independent random samples of n 1 and n 2 observations are selected from normal populations. Further, assume that the populations possess a common variance σ 2 . a) Show that the pooled estimator S 2 is unbiased. b) Find Var(S 2 ). 6. Note that the small-sample confidence interval for μ , based on t distribution possesses a random width. Find the expected value of the interval width in the small sample case. 7. A random sample of size 2 is selected from a normal population with mean 0 and variance
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Unformatted text preview: σ 2 , further assume x 1 = -0.75, x 2 = 0.16. How sure (or confident) would you be that a) σ 2 > 1.0221 ? b) σ 2 > 0.4242 ? c) σ 2 > 2.7909 8. Exercise 7.38 in page 392. 9. Let x 1 , x 2 , …, x n be a random sample of n observations from an exponential distribution with mean β . Derive large-sample confidence interval for β . 10. Let X 1 , X 2 be a random sample of a random variable X whose density is exponential with parameter θ = 1. a) Show that X 1 / X 2 has an F distribution with degrees of freedoms 2 and 2. b) Find a and b such that P(X 1 / X 2 < a) = 0.95, P(a < X 1 / X 2 < b) = 0.04 11. Exercise 6.68 in page 357 of the textbook. 12. Exercise 6.69 in page 357 of the textbook. 13. Exercise 7.36 in page 391 of the textbook. 14. Exercise 7.40 in page 392 of the textbook....
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