Prac_Quiz1 - ST 561 Preparation for Quiz 1(not to hand in...

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Unformatted text preview: ST 561: Preparation for Quiz 1 (not to hand in) 1. (The Infamous Monty Hall problem). There are 3 doors. Behind one door is a car; behind the other two doors there are goats. You choose one door. Monty Hall opens another door and a goat appears — then he asks you if you want to switch and choose the remaining door. Should you switch? ' 2. 'vao dice are rolled. X = # of spots on die 1; Y = #z of spots on die 2. Let Z 2 X + Y. Find P(X > 1|Z :4) and P(Z 2 4|X > 1). 3. In a lot of 50 light bulbs, there are two bad bulbs. An inspector examines five bulbs, which are selected at random and without replacement. a. Find the probability of at least one defective bulb among the five. b. How many bulbs should be examined so that the probability of finding at least one bad bulb exceeds 1/2? 4. If f(.'1:) : c(2/3)‘” for 53 z 1, 2,2, ...., find the value of c that makes f(a:) a probability mass function. ...
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