1. Suppose we are selling cups of lemonade. If the weather is good, we believe the demand D will have a Poisson distribution with mean 20. If the weather is not good, we believe the demand will be geometric with mean 5. The weather is predicted to be good with probability 6/10. Let G denote the event that the weather is good.
2. (a)Express the following in symbols: the demand.
3. (b)Express the following in symbols: the expected demand.
4. (c)Express the following in symbols: the expected demand given that the weather is good.
5. (d)Express the following in symbols: the probability that the demand is 3.
6. (e)Express the following in symbols: the probability that the demand is 3 given that the weather is good.
7. (f)Compute the probability that the demand is 3 given that the weather is good.
8. (g)Compute the probability that the demand is 3.
9. (h)Compute the expected demand given that the weather is good.
10. (i)Compute the expected demand.
11. (j)Your approach to computing the expected demand corresponds to an equation in Chapter 2 of Hajek. What is that equation?
12. (k)Compute P{G | D = 0}.
13. (l)Compute P{G | D = 1}.
14. (m)Compute P{D is odd | G}.
15. (n)Compute P{D is odd | Gc}.