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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Homework 3 EXERCISE 1 Use the binomial theorem (go back to your classnotes from the beginning of the course) to show that if X b ( n,p ) then n x =0 p ( x ) = 1. EXERCISE 2 New York Lotto is played as follows: Out of 59 numbers 6 are chosen at random without replacement. Then from the remaining 53 numbers 1 is chosen. This last number is called the bonus number. You, the player, select 6 numbers. To win the first prize you must match your 6 numbers with the States 6 numbers. If you match only 5 numbers and your 6 th number matches the bonus number then you win the second prize. a. What is the probability of winning the first prize? b. What is the probability of winning the second prize? c. What is the probability of winning a prize (either the first or the second)? Note: Check your answers to ( a,b ) at http://www.nylottery.org/games/lotto.php ....
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