Econ 101 ( assignment 1)

Assignment 2

1. A small brewer has two bottling machines. Machine A produces 75% of the bottles, and machine B produces 25% of the bottles. 1 out of 20 bottles filled by A is rejected for some reason, wile 1 out of every 30 bottles from B id rejected. What is the probability that a randomly selected bottle comes from machine A, given that is accepted?
2. A municipal bond service has three rating categories (A, B, and C) and is issued by city or suburbs. Suppose that 70% of all the issued bonds were A rated, 20% of all the issued bonds were B rated, and 10% of all the issued bonds were C. Of the municipal bonds rated A, 50% were issued by cities. Of the municipal bonds rated B, 40% were issued by cities. Of the municipal bonds rated C, 50% were issued by cities.

1. If three bonds are selected at random, list the sample space indicating the possible rating categories for all three.
2. What is the probability that a bond issued by suburbs?
3. What is the probability that a bond issued by suburbs and rated B?
4. Given a bond is issued by a city what is the probability that is rated B?

3. The director of publications for a university is in charge of deciding how many programs to print for football games. Based on the data, the director has estimated the following probability distribution for the random variable X= number of programs sold at the university football game:

X             25,000                   40,000                   55,000                   70,000

P(X)       0.1                          0.3                          0.45                        0.15

1. Compute the expected number of program sold at the university football game.
2. Compute the variance of program sold at the university football game.
3. Each program cost $1.25 to print and sells for $3.25. Any programs left unsold at the end of the game are discarded. The director has decided to print ether 55,000 or 70,000. Which of these two options maximizes the expected profit from program sale?

4 . An investor has $10,000 invested in asset (X). His advisor recommend a new asset( Y) for investment with following  rate of returns and probabilities:

a.) Do you agree with the advisor recommendation to invest in asset Y? Explain.

b.) If the investor able to divide his money and put it in a new portfolio: $5,000 (50%) in asset (X) and $5,000 (50%) in asset (Y). Would you recommend the new portfolio? Explain.