Temple University
Department of Economcs
Economics 8009
1. The table gives daily sales of cars by a local dealership, from a 0 minimum to a 6 maximum, and the number of days for which that number of sales happened during a 100day survey. That is, 0 cars were sold on 6 days, 1 car on 8 days, etc.
Cars per Day 
0 
1 
2 
3 
4 
5 
6 
Number of days 
6 
8 
22 
20 
15 
16 
13 
(a) Enter the probability density in the following table:
Car Sales per Day, X 
0 
1 
2 
3 
4 
5 
6 
f(x) 
(b) Compute the expected value of X and give its meaning.
(c) Compute the varaince and standard deviation of X.
2. The following table gives data on 100 observations on 3 mutual funds, Y, with the average rates of return, X, of 6%, 5%, and 10%.
Y 

1 
2 
3 

X 
6 
0 
10 
15 
5 
10 
15 
20 

10 
25 
5 
0 
(a) Find the marginal probability functions of X and Y. Enter your answer in the table below.
Y 

1 
2 
3 

X 
6 

5 

10 

(b) Find the conditional probability density function of X given that Y equals 3.
(c) Find the covariance of X and Y.
(d) Verify if X and Y are statistically independent.
3. Let Z be a standard normal variable. Find:
(a) P(Z > 0.54)
(b) P(0.35<Z<1.67)
4. Suppose a mutual fund has an annual rate of return that is approximately normally distributed with mean 7% and variance 64.
(a) Find the probability that the annual return will be negative.
(b) Find the probability that an annual return will exceed 10%.
5. Prove that if A and B are mutually exclusive then .
6. Prove that is a cdf. Along the way you will have to state the support of the cdf.