Question: Modify the critical regions on pages 365 and 366 so
Modify the critical regions on pages 365 and 366 so that they can be used to test the null hypothesis λ = λ0 against the alternative hypotheses λ > λ0, λ < λ0, and λ ≠ λ0 on the basis of n observations. Here λ is the parameter of the Poisson distribution.
Answer to relevant QuestionsWith reference to Example 14.1, show that the regression equation of X on Y is Also sketch the regression curve. In Example 14.1 Given a pair of random variables X and Y having the variances σ21 and σ22 and the correlation coefficient ρ, use Theorem 4.14 to express var(X/s1 + Y/s2) and var(X/s1 – Y/s2) in terms of σ1, σ2, and ρ. Then, making ...Show that (a) ∑2, the random variable corresponding to 2, is not an unbiased estimator of σ2; (b) S2e = n·∑2 / n–2 is an unbiased estimator of σ2. The quantity se is often referred to as the standard error of ...Use the results of Exercises 14.20 and 14.21 and the fact that E(Bˆ) = β and var(Bˆ) = σ2/ Sxx to show that Y0 – (Aˆ + Bˆx0) is a random variable having a normal distribution with zero mean and the variance Here Y0 ...Verify that under the assumptions of normal multiple regression analysis (a) The maximum likelihood estimates of the β’ s equal the corresponding least squares estimates; (b) The maximum likelihood estimate of s is
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