1. There are 30 students enrolled in this class. Suppose Hi is the height of the ith student. What is the range of values for i? Is Hi a random variable?

2. The following is the joint probability distribution of number ofcar crashes (C) and car make (M).

C = 0 C = 1 C = 2 C = 3 C = 4

TOYOTA (M = 0) 0.35 0.065 0.05 0.025 0.01

OTHER (M = 1) 0.45 0.035 0.01 0.005 0.00

A.Report the marginal probability distribution for C

B.What is the average number of car crash?

C.What is the variance of the number of crashes?

D.Calculate CM and CM.

3. Suppose car manufacturers are penalized (P) on the basis of the following formula

P = 60,000 + 6C - 2M

Using your answers for Question 7, calculate the following

The average penalty (P)
The variance of penalty (P)

4. X and Y are two random variables. The average value of X is 40,000 and X has a standard deviation of 12,000. The average value of Y is 45,000 and the standard deviation of Y is 18,000. The correlation between X and Y is 0.80.

Let C = X + Y

Calculate

E(C)

Cov(XY)

Var(C)

5. The random variable Y has a mean of 1 and a variance of 4.

Let Z = ½(Y - 1)

Calculate µZ and ?Z2.