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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so for some reason I couldn't add my answer so I screenshot it and added it below uhh hope it helps!
Answer:
255
Step-by-step explanation:
The n th term of a geometric series is
= a
where a is the first term and r the common ratio
1 ← is the n th term
with a = 1 and r = 2
The sum to n terms of a geometric series is
=
, thus
=
= - 1 = 256 - 1 = 255