Section One: Basics
1. The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.
|
# of claims
|
2
|
3
|
4
|
5
|
6
|
7
|
|
P(x)
|
0.11
|
0.16
|
0.27
|
0.23
|
0.13
|
0.10
|
What is the variance of the number of claims processed?
2. A company hires management trainees for entry level sales positions. Past experience indicates that only 20% will still be employed at the end of nine months. Assume the company recently hired six trainees.
What is the standard deviation of the number of trainees that will still be employed at the end of nine months?
3. The following table displays the joint probability distribution of two discrete random variables X and Y.
|
x
|
|
y
|
|
1
|
2
|
3
|
|
0
|
0.10
|
0.12
|
0.06
|
|
1
|
0.05
|
0.10
|
0.11
|
|
2
|
0.02
|
0.16
|
0.28
|
Compute the variance for the linear function
a) W=3+4 X , W=5+10Y, W=a+bY
b) W = 2X + Y.
4. Do end of Chapter 4 practices: 4.100,4.95, 4.96, 4.100, (page 172 - 173)
5. Do end of Chapter 5 practices: 5.19, 5.22, 5.25, 5.65, 5.66, 5.72, 5.97,5.98
6. Please do the practice question 4.45 (Page 146) from your text book. Then think carefully about the relationship between Bernoulli distribution and Binomial distribution, show how we can get the mean and variance of a Binominal distribution using the relations between them.
SectionTwo: Computer Exercise
(I will explain how to do the question in lecture time. You may prepare yourself tying to explore how to answer the following question.)
Generate one series of data for Bernoulli distribution, Binomial Distribution, Uniform distribution and Normal distribution with the Random Number Generator from Excel as shown in Class. The number of data points for each series should be 100.
(1) Please write down the probability distribution function of your data.
(2) Generate 50 series for each of the distribution in question one, then calculated the average of each series, we call this sample averages. Now that you have 50 sample averages, plot the histogram of youraverage (to save time, use the automatically assigned bin range). Then answer the following question
a. How does your histogram assemble the probability distribution of normal distribution?
b. What is the average of the sample averages? What is mean of your sample averages? Compare with your population data.