Concert attandance 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 expacted to be 500 people if the weather is terrible, 1000 people if the weather is mediocre, and 2000 people if the weather is great.
(a) Let X denote the attendance. Why is X a random variable?
(b) What is the expected attendance, E(X)?
(c) 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?
(d) Find the standard deviation of profit Y.