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?
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.
For this case we have a function of the form: y = A * (b) ^ t Where, A: initial amount b: growth rate t: time Substituting values we have: y = 1000 * (3) ^ ((1/8) * t) For 24 years we have: y = 1000 * (3) ^ ((1/8) * 24) y = 27000 Answer: D) 27,000; exponential