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The instructions and problems for the midterm exam of math 5010 - probability theory, fall 2004. The exam covers topics such as poisson distribution, distribution functions, uniform distribution, and inverse trigonometric functions.
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Midterm 2B – Math 5010 – Fall 2004
Name:
Instructions. READ CAREFULLY. :
(i) The work you turn in must be your own. You may not discuss the midterm with anyone, either in the class or outside the class. [You may of course consult with me for clarifica- tion of any of the problems.] Failure to follow this policy will be considered cheating and will result in a course grade of E.
(ii) You may consult the textbook and your notes. You may consult a textbook on calculus. You may not use any other written source. Failure to follow this policy will be consid- ered cheating and will result in a course grade of E. (iii) Your midterm must be clearly written and legible. I will not grade problems which are sloppily presented and such problems will receive a grade of 0. If you are unable to write legibly and clearly, use of a word processor. Budget time for writing up your solu- tions. (iv) Think about your exposition. Someone (me) has to read what you have written. Your answer is only correct if I can understand what you have done. I reserve the right to deduct points for style, grammar, and spelling.
(v) Midterms are due at Monday November 1 at 9:40. Late midterms will not be accepted.
Sign below to indicate you have read and understand these instructions.
STOP! Did you read the instructions and sign where indicated? If not go back and do it now.
Problem 1. Let X have a Poisson( λ ) probability mass function. Find
E
Problem 3. You break into two a one meter stick at a random location which is uniformly distributed. Let L be the length of the smaller piece. Find V ( L ).
Problem 4. Suppose that the arrivals of airplanes at an airport satisfies the hypotheses of a Poisson process. Planes arrive at the rate of 1 every 2 minutes. What is the probability that in 3 out of 7 days, there are no arrivals from 10 : 00 AM to 10 : 04 AM.