Two different plasma etchers in a semiconductor factory have the same mean etch

Question

Two different plasma etchers in a semiconductor factory have the same mean etch rate . However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine l is , and for machine 2 is - . Suppose that we have a sample of n independent observations on etch rate from machine 1 and n2 independent observations on etch rate from machine 2, and that the samples are independent. Find the bias of the estimator ,- Xi + X2. (a) (b) 0 (c)c (d) (e)t

Explanation / Answer

X1/3+ 2/3 (X2) = 1/3(mu) + 2/3*(mu) = mu.

So option A is correct.

b)

Var(mu) = Var(1/3(X1) + 2/3(X2)) = Var(1/3(X1)) + Var(2/3(X2)) (Since two are indepedent)

= 1/9* Var(X1) + 4/9*(Var(X2) = 1/9* (sigma1^2/n1) + 4/9* (sigma2^2/n2) = 1/9*(sigma1^2/n1 + 4/3sigma2^2/n2)

SD = 1/3 *sigma* SQRT(1/n1 + 4/3*n2)

Option e is correct

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