Suppose a family has saved enough for a 10 day vacation (the only one they will be able to take for 10 years)and has a utility function U = V^1/2 (where V is the number of healthy vacation days they experience).Suppose they are not a particularly healthy family and the probability that someone will have a vacation-ruining illness (V = 0)is 20%.What is the expected value of V? A) 10 B) 8 C) 2 D) 0

Question

Quizplus · Accepted Answer

To find the expected value of V, we need to calculate the probability-weighted average of all possible values of V.

Let's consider the two possible outcomes: 
1. The family experiences a healthy vacation (V = 1), with probability 80%. 
2. The family experiences a vacation-ruining illness (V = 0), with probability 20%.

Expected value of V = (probability of V=1 * V=1) + (probability of V=0 * V=0) 
Expected value of V = (0.8 * 1) + (0.2 * 0) 
Expected value of V = 0.8

So, the expected value of V is 0.8, which means that on average, the family is expected to have 0.8 healthy vacation days out of 10.

However, since we cannot have fractional vacation days, the best choice would be to round down to 0 healthy vacation days, which is V=0. This ensures that the family is not disappointed if they have no healthy vacation days, and they can still be pleasantly surprised if they manage to have any healthy vacation days at all. Therefore, the best choice is:

Answer: B (0 healthy vacation days)

Suppose a Family Has Saved Enough for a 10 Day