# Calculating the expected value

#### Ayyappa

##### New Member
Hi, I have a strange problem. Following info is provided:
Event insurance comp. allows promoters of any event to protect themselves from financial losses due to uncontrollable circumstances like rainouts. Each spring Dallas' downtown council puts an event. This year it is a rainy time in Dallas and chance of receiving an inch or more rain during weekend is one out of 4. The policy would pay $10000 if it rained more than an inch. Policy amount is$650.
Determine whether or not you believe that these dollar amounts are correct?

How to find the expected value of the profit made by the company?

#### BGM

##### TS Contributor
If the company pay nothing when Dallas receiving less than an inch of rain,
then the expected payoff of the company
$$= (\10000)(\frac {1} {4}) + (\0)(\frac {3} {4}) = \2500 > \650$$
In this way the company is expected to lose money
I am curious whether "during weekend" have any implication, e.g. to divide by 7.

For discrete distribution, the formula for evaluating expected value is
$$E[X] = \sum_x x Pr\{X = x\}$$