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Quiz1 - AMS312.01 Quiz 1 Spring 2010 Name ID Signature...

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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 12:50-2:10pm. 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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