{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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)...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern