4.8 (Stratified sampling) Let D be a training set with only 10 examples, whose labels are 1, 1, 2,2,2, 2,2, 2, 2,2, respectively. This dataset is both small in size and imbalanced. We need cross-validation during evaluation, and 2-fold CV seems a good choice. (a) Write a program to randomly split this dataset into two subsets, with five examples in each subset. Repeat this random split 10 times. The histogram of class 1 examples in these two subsets can be (0,2) or (1,1)-one subset has zero (two) and the other has two (zero) class 1 examples, or every subset has exactly one class 1 example. In your 10 splits, how many times does (0,2) appear? (Note: This number can be different if you perform the experiments multiple times.) (b) What is the probability that (0,2) will appear in one random split of these 10 examples? (c) In your 2-fold CV evaluation, if the split's class 1 distribution in the two subsets is (0,2), how will it affect the evaluation? (d) One commonly used way to avoid this issue to use stratified sampling. In stratified sampling, we perform the train/test split for every class separately. Show that if stratified sampling is used, the distribution of class 1 examples will always be (1,1)