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ps3 - Bernoulli trial is an experiment whose outcome is...

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EE 497B PROBLEM SET 3 DUE: 26 Feb 2008 Reading assignment: Ch 2. Problem 18: (10 points) The number of k - combinations of n objects is denoted as n k , which is read as n choose k and is calculated as n k = n ! k !( n - k )! . In the branch of mathematics known as combinatorics, n k is called a binomial coefficient as it represents the expansion of the binomial ( x + y ) n = n k =0 n k x n - k y k . 1. (3 points) Explicitly expand ( x + y ) 4 by multiplication, and compare your result to ( x + y ) 4 = 4 0 x 4 + 4 1 x 3 y + 4 2 x 2 y 2 + 4 3 xy 3 + 4 4 y 4 . Pascal’s triangle provides a convenient means for determining the binomial coefficients without calculating factorial: 1 1 , 1 1 , 2 , 1 1 , 3 , 3 , 1 1 , 4 , 6 , 4 , 1 .......... Construct Pascal’s triangle by starting with ones at the outside and then always adding two adjacent numbers and writing the sum directly underneath. In this way, the triangle can be extended for an arbitrary number of rows. The elements of the n th row are n 0 n 1 · · · n n . 2. (7 points) In the study of probability, a
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Unformatted text preview: Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, ”success” and ”failure”. Let p denote the probability of a success, and q = 1-p the probability of a failure. A Binomial experiment consists of n independent Bernoulli trials, where the probability of a successes, p , is constant from trial to trial. Determine the probability of achieving k success in A Binomial experiment. Problem 19: Yates Problem 2.2.4 (12 points) Problem 20: Yates Problem 2.3.2 (12 points) Problem 21: Yates Problem 2.3.7 (12 points) Problem 22: Yates Problem 2.3.11 (15 points) Problem 23: Yates Problem 2.4.1 (12 points) Problem 24: Yates Problem 2.5.3 (12 points) Problem 25: Yates Problem 2.10.1 (15 points)...
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