Exercise 4.4

1.

Let S denote the sum of two numbers spun on a fair spinner with the numbers 1, 2, and 3 on it. The range of S is 2, 3, 4, 5, 6. Determine the probability model variance of S.

2.

Let X denote the number of aces in a 2 card hand drawn without replacement from a well shuffled standard deck 0f 52 cards. Then the range of X is {0, 1, 2}. Determine the probability model variance of X.

3.

Repeat the last problem under sampling with replacement.

4.

In the urn problem (with the balls well mixed ) discussed above, let Z denote the number of red balls in the sample (without replacement) of size 3. Determine the probability model variance of Z.