Concert attendance depends on the weather. There are three possible types of weather on the day of the concert: terrible, with probability 20%, mediocre, with probability 60%, and great, with probability 20%. Concert attendance is expected to be 500 people if the weather is terrible, 1000 people if the weather is mediocre and 2000 people if the weather is great. Let X denote the attendance.
(a) What is the expected attendance, E(X)?
(b) Suppose that each ticket costs $5 and the total cost of giving the concert is fixed and equal $2000. Then, if Y denotes profit from the concert, we have Y = 5X − 2000. What is the expected profit?
(c) Find the standard deviation of profit Y.