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AMS312.01
Quiz 1
Spring 2010 ♠♣♥♦
Name: ________________________________ ID: ____________________ Signature: ________________________
Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide
complete solutions for full credit. The exam goes from 12:502:10pm. Good luck!
1.
For a random variable following the normal distribution with mean μ and variance σ
2
, please derive its moment
generating function.
2.
Suppose you are on a game show, and you are given a choice of three doors. Behind one door is a car, behind the
others, nothing. You would win if you have chosen the door with the car behind it. After you have chosen a door (say,
door #1), the host, who knows what’s behind the door, would reveal one of the other two doors, and he would always
choose one with nothing behind it, (say door #3). Then he would ask you, “Would you like to pick the other unopened
door (say door #2) instead?”
(a) What is the chance of winning if you do switch?
(b) What is the chance of winning if you do not switch?
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This note was uploaded on 11/14/2010 for the course AMS 312 taught by Professor Zhu,w during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Zhu,W

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