Question: If X1 and X2 are independent random variables having binomial
If X1 and X2 are independent random variables having binomial distributions with the parameters θ and n1 and θ and n2, show that X1 + X2 / n1 + n2 is a sufficient estimator of θ.
Answer to relevant QuestionsIn reference to Exercise 10.43, is X1 + 2X2 / n1 + 2n2 a sufficient estimator of θ? Show that the estimator of Exercise 10.5 is a sufficient estimator of the variance of a normal population with the known mean µ. Exercise 10.5 Show that is a minimum variance unbiased estimator of the mean µ of a normal ...Use the results of Theorem 8.1 on page 233 to show that 2 is an asymptotically unbiased estimator of µ2. Use the method of maximum likelihood to rework Exercise 10.57. In Example 10.19 the prior distribution of the parameter of the binomial distribution was a beta distribution with α = β = 40. Use Theorem 6.5 on page 182 to find the mean and the variance of this prior distribution and ...
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