1. Find the number of ways the following can happen. Suppose that you can buy tw

Question

1. Find the number of ways the following can happen. Suppose that you can buy two types of cars such that you can get one in four colors and the other in 5 colors, each car comes in a basic or luxury edition. How many different cars (different colors and luxury or basic count as different cars can you buy?

2. Suppose that I have a manufacturing plant that creates iron rods that are 10 inches long. If the average length is 10 inches long and has a standard deviation of .05 inches. A.) Suppose that I am interested in the outcome of the average 20 inch rods made by the same process. That is, if each are independently produced, I am interested in Y=sum i=1 to n (Xi/n) What is the expected value for the average of the 20 rod and the variance Y?

B.) What is the distribution of Y? What is the P(Y<9.95 inch)?

3. Consider the following joint distribution of x and y. f(x,y)=(x+2)(1/8) if 0<x<2, 0<y<1 and f(x,y)=(x+y+2)(1/44) 2<x<4, 0<y<1. It is 0 otherwise.

A.) Find E(XY).

B.) find the marginal distribution for y

Explanation / Answer

1.

First car has 4 colors and 2 types basic and luxury so the number of ways of buying first car is

4*2 = 8

Second car has 5 colors and 2 types basic and luxury so the number of ways of buying second car is

5*2 = 10

Since both cars are independent from each other so total number of ways of buying four cars is

10 *8 = 80

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