2. Refer to Exercise 1.

(a) Select two wafers, at random and with replacement, from the batch of 10 wafers given in the exercise.

(i) Give the sample space for the experiment that records the doping type of the two wafers and the probability for each outcome.

(ii) Give the sample space of the experiment that records the number of n-type wafers among the two selected and the corresponding probability mass function.

(b) Select four wafers, at random and with replacement, from the batch of 10 wafers given in the exercise.

(i) Give a verbal description of the sample space for the experiment that records the doping type of the four wafers, find the size of the sample space using the R commands G=expand.grid(W1=0:1,W2=0:1,W3=0:1,W4=

0:1); length(G$W1), and give the probability of each outcome.

(ii) Give the sample space of the experiment that records the number of n-type wafers among the four selected and the corresponding PMF using the additional R commands attach(G);

table((W1+W2+W3+W4)/4)/length(W1).

(iii) Use the probability mass function to find the probability of at most one n-type wafer among the four selected.