20.17 The Asian stochastic beetle. We met this insect in Exercise 19.21 (page 460). Females have this probability model for their number of female offspring:
| Offspring: | 0 | 1 | 2 |
| Probability: | 0.2 | 0.3 | 0.5 |
(a) What is the expected number of female offspring?
(b) Use the law of large numbers to explain why the population should grow if the expected number of female offspring is greater than 1 and die out if this expected value is less than 1.