Suppose that W1 is a random variable with mean μ and variance σ21 and W2 is a random variable with mean μ and variance σ2. From
Example 5.4.3, we know that cW1 + (1 − c)W2 is an unbiased estimator of μ for any constant c > 0. If W1 and W2 are independent, for what value of c is the estimator cW1 + (1 − c)W2 most efficient?
1 answer:
Answer:
Step-by-step explanation:
The concept of variance in random variable is applied in solving for the value of c for the estimator cW1 + (1 − c)W2 to be most efficient. Appropriate differentiation of the estimator with respect to c will give the value of c when the result is at minimum.
The detailed analysis and step by step approach is as shown in the attachment.
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Answer: $100,000
<u>Step-by-step explanation:</u>
Land + Stocks + Bonds + Savings = 100%
+ 0.1x +
+ 35,000 = 1.00x
= 0.5x + 0.1x + 0.05x + 35,000 = 1.00x
= 0.65x + 35,000 = 1.00x
35,000 = 0.35x
100,000 = x