# Question: If 1 is the mean of a random sample of

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 the two samples are independent, show that

(a) ω ∙ 1 +(1 – ω) ∙ 2, where 0 ≤ ω ≤ 1, is an unbiased estimator of µ;

(b) The variance of this estimator is a minimum when

(a) ω ∙ 1 +(1 – ω) ∙ 2, where 0 ≤ ω ≤ 1, is an unbiased estimator of µ;

(b) The variance of this estimator is a minimum when

**View Solution:**## Answer to relevant Questions

With reference to Exercise 10.21, find the efficiency of the estimator of part (a) with ω = 1/2 relative to this estimator with In exercise If 1 is the mean of a random sample of size n from a normal population with the ...Verify the result given for var(n + 1 / n ∙ Yn) in Example 10.6. Use Definition 10.5 to show that Y1, the first order statistic, is a consistent estimator of the parameter α of a uniform population with β = α + 1. Definition 10.5 The statistic is a consistent estimator of the ...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. If X1, X2, . . . , Xn constitute a random sample of size n from a population given by Find estimators for ∂ and θ by the method of moments. This distribution is sometimes referred to as the two-parameter exponential ...Post your question