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Assignment2

# Assignment2 - 1 Assignment 2 STAT220-Winter 2011 Instructor...

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1 Assignment 2, STAT220-Winter 2011 Instructor: Kamyar Moshksar Due on Wednesday, Feb. 9th Problem 1 - In your course notes, you can find the following identity at the end of section 3 in the “Review of Useful Series and Sums” subsection: min { a,n } X x =max { 0 ,n - b } a x b n - x = a + b n . ( * ) This identity is proved in your course notes using Binomial Expansion. In this problem, you will prove this identity probabilistically. We have a box that contains a + b bulbs where a bulbs are defective and the rest ( b bulbs) are fine. We pick n bulbs at random. (a) what is the probability that exactly x of the n picked bulbs are defective? (b) Prove the identity in (*) using the result in part (a). Problem 2- We have a coin with the property that P( Head ) = p and P( Tail ) = 1 - p . This coin is tossed repeatedly and independently until a Tail appears for the first time. Find the probability that the number of required tosses is even? Problem 3- A standard pack of cards has 52 cards, 13 in each of four suits. Suppose 4 players are dealt 13 cards each from a well-shuffled pack. What is the probability of dealing a perfect hand? (13 of

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Assignment2 - 1 Assignment 2 STAT220-Winter 2011 Instructor...

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