1 for each of the following two parts you must justify your

Assignment Help Microeconomics

Reference no: EM13375918

1. For each of the following two parts, you must justify your answer. No explanation = no credit. Partially correct explanations=partial credit.

a) True or false. For the events A and B, if (A'∩B') = Ø , then the events are exhaustive.

b) True or false. For two events A and B, if P(A)=.3, P(B)=.25, and P(AUB)=.50, then A and B are mutually exclusive.

2. A raffle is being held at a school to raise money for the library. The organizers sell 40 tickets. They will select 4 winning tickets at random for prizes.

a) How many different combinations of 4 winning tickets can there be?

b) Suppose you hold 6 tickets. What is the probability that you will win exactly 2 out of the 4 prizes.

3. Let the random variable R denote the rate of return on an asset. R has the following pdf.

R	P(R=r)
.3	.05
.2	.20
.1	.20
0	.20
-.1	.15
-.2	.10
-.3	.10

a. What is the expected value and variance of R?

b. You are considering investing $150 in this asset. After 1 year, the value will be $150(1+R). What is the expected value and standard deviation of the value of your asset in 1 year?

4. Suppose the random variable X has a mean of 16 and a variance of 144. Y is a linear transformation of the form Y=a+bX. Y has a mean of 4 and variance 36. Assuming b>0, what are the values of a and b?

5. Suppose cell phones are available in two basic types: Flashy or Dull. Furthermore, suppose cell phone owners fall into two basic categories: Hipsters or Grannies.

Let .55 be the probability of being a Hipster. Also, 40% of cell phones are both Flashy and owned by Hipsters. Finally, if a cell phone is owned by a Granny, the probability of it being Dull is .90

a) What is the probability that a cell phone is both Dull and owned by a Hipster.

b) If a phone is owned by a Hipster, what is the probability it is Flashy.

c) What is the probability that any randomly chosen phone is Dull?

6. Suppose a microchip manufacturer produces 1 defective chip for every 30 they build. They randomly select 210 chips off the assembly line for quality control testing.

a) What is the expected value and variance of the number of defective chips?

b) What is the probability that they discover exactly 9 defective chips in this test?

7. On a typical spring afternoon, customers enter a bookstore at a rate of 80 per hour.

a. What is the value of λ, defined as the average rate of customers per minute?

b. In 30 minutes, what is the a) expected value and b) standard deviation of the number of customers entering the store?

c. In a 3 minute period, what is the probability of 2 or more customers entering the store?

Reference no: EM13375918

Questions Cloud

Production in the long-runsuppose the production function : production in the long-runsuppose the production function of a typical producer is given as where l is labor and k is

Profit maximization in short-runa jeans manufacturer hires : profit maximization in short-runa jeans manufacturer hires workers to sew jeans in its factory and derives the

Instructions unless otherwise stated all true or false : instructions unless otherwise stated all true or false questions require graphical illustration. properly drawn graphs

You were appointed to manage the production facility of : you were appointed to manage the production facility of your new factory in saint john. a think tank estimated the

1 for each of the following two parts you must justify your : 1. for each of the following two parts you must justify your answer. no explanation no credit.nbsp partially correct

In 1989 the detroit free pressand detroit daily newsthe : in 1989 the detroit free pressand detroit daily newsthe only daily newspapers in the city obtained permission to merge

Over the last 30 years in the united states the real price : over the last 30 years in the united states the real price of a college education i.e. after adjusting for inflation

Consider the five basic methods of payment for : consider the five basic methods of payment for international trade. describe the pros and cons of each. if your company

Question 1the demand for watermelons is highest during : question 1the demand for watermelons is highest during summer and lowest during winter. yet watermelon prices are

User Account

All Pages