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 100-day 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.