Question: Verify the results given on page 273 for the marginal
Verify the results given on page 273 for the marginal density of X and the conditional density of given X = x.
Answer to relevant QuestionsSuppose that we want to estimate the parameter θ of the geometric distribution on the basis of a single observation. If the loss function is given by And Θ is looked upon as a random variable having the uniform density ...Show that the sample proportion X/n is a minimum variance unbiased estimator of the binomial parameter θ. If 1 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ21, 2 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ22, and ...With reference to Exercise 10.12, show that 2X – 1 is also an unbiased estimator of k, and find the efficiency of this estimator relative to the one of part (b) of Exercise 10.12 for (a) n = 2; (b) n = 3. Use the result of Example 8.4 on page 253 to show that for random samples of size n = 3 the median is a biased estimator of the parameter θ of an exponential population.
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