=========================preview======================
(MATH144)[2004](f)midterm2~4660^_88499.pdf
Back to MATH144 Login to download
======================================================

MATH 244 Applied Statistics


Mid-Term Test II October 29, 2004




Please read the following instructions carefully before you begin the exam.


1. Do not begin until you are told to do so.

2. Please place your student identity card on your desk for verification purposes.

3. There are 5 questions in this test. You have to answer all questions. Please write down all your answers in your answer book. Show all your works.



4. You will have 1 hour and 30 minutes to complete the exam.

5. No books, notes or other reading materials are permitted. Some formulae and statistics tables that you may need are provided.

6. If you feel you need to think a lot for a question, skip it and return to it later. Some of the easiest question for you might be at the very end. So, choose your own order of answering the questions.

7. Anyone who is caught cheating, helping someone cheat, or who is suspected of cheating, will receive zero mark on this exam. There will be no exception.

8. Do your best, and good luck!!!














1. (20 marks) A game uses two fair dice. To participate, you pay $20 per roll. You win $10 if the total is even number, $42 if the total is 7, and $102 if the total is 11. The game is fair if your expected net gain is zero.

(a)
Let X be the net gain for one roll. Find the pmf of X.
(5 marks)





(b)
Is the game fair? Why?
(5 marks)





(c)
What is the standard deviation of your gain?
(5 marks)





(d)
What is the chance that you will lose money after 50 independent games?
(5 marks)




2. (18 marks)
(a)
State the three assumptions of Poisson process.
(8 marks)





(b)
Without using any mathematical expression, verbally describe the memoryless property.
(5 marks)





(c)
Write down the definition of an unbiased estimator.
(5 marks)




3. (18 marks) Suppose that bad records appear in a used computer tape at a rate of 5 per 200 feet, in accordance with a Poisson process. Let W be the number of feet at which the fourth bad record is found.

(a)
On average how many flaws can be found in one foot of tape?
(3 marks)





(b)
Find the probability that there will be less than three flaws found in 150 feet of tape.
(4 marks)





(c)
Write down the distribution of W.
(3 marks)





(d)
If it was found that there are less than four flaws in the first 70 feet, what is the probability that the fourth flaw will be found beyond 310 feet?
(8 marks)




P. T. O.
4. (22 marks) A manufacturer of diesel engines found that the diameters of the cylinders drilled into an engine block vary slightly. They are normally distributed around the target value of 12.5cm, with a standard deviation of 0.002cm. A cylinder with diameter within 0.003cm of its