2. (a) (b) Wet chemical etching is commonly used in semiconductor production to remove silicon from the backs of wafers

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2 A B Wet Chemical Etching Is Commonly Used In Semiconductor Production To Remove Silicon From The Backs Of Wafers 1 (77.92 KiB) Viewed 11 times

2. (a) (b) Wet chemical etching is commonly used in semiconductor production to remove silicon from the backs of wafers before metalisation. The etch rate is a crucial aspect of this procedure. The effectiveness of two distinct etching solutions is being investigated. Ten randomly selected wafers have been etched in each solution and the observed rates (in mils/min) are as follows. Solution A 10.6 10.2 10.5 10.1 10.9 9.7 9.5 10.0 10.4 9.9 Solution B 10.4 10.4 10.5 10.3 10.9 11.0 11.0 (i) (ii) 10.7 10.9 10.3 Assume that the etch rates of both etching solutions are normally distributed with unknown means and variances. Further assume that both etching solutions have equal variances. (i) Construct a 95% confidence interval of the difference in mean etch rate for the two solutions. (ii) At the 5% significance level, test the null hypothesis that the difference between the mean etch rates of solution A and solution B is 0.1. (9 marks) Let X₁, X2,..., X₁ denote independent and identically distributed random variables from a distribution with pdf given by f(x) = (²) rx²-¹e-x/ex>0, where > 0 is an unknown parameter and r is a known positive constant. Show that the maximum likelihood estimator of 0 is 0=Xi Show that Ô is an unbiased estimator of 0. Given the following observations, find the maximum likelihood estimate of 0 when r is 3: 1.4, 2.3, 3.0, 2.4, 3.5, 4.3 (10 marks)