Notes_for_19th_feb

# Notes_for_19th_feb - The hypergeometric probability...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The hypergeometric probability distribution Suppose a population of N units has a of the N possessing a certain characteristic, N—a not possessing the characteristic (a 2 outcome setup). A sample of n units is to be selected from the population without replacement. (There are a “S outcomes” and N—a “F outcomes in the population). The random variable of interest is X, the number of units in the sample possessing the characteristic. X is called a hypergeometric random variable and its f(X) is denoted h(x;n,a,N), a three parameter probability distribution. h0gn¢gN)=—E-l::£—gxzﬁhh2wunmﬁan)(ummﬂyn) (if) Notel: In acceptance sampling(lot sampling, inspection sampling), N is the lot size, a is the number of defectives in the lot, n is the sample size, and f(x) is the probability of exactly X defectives in the sample. 114a Note2: From Vandermonde’s theorem, 2 : vox n—x n ihﬁhngyN):l. x20 ' - :b- :/N Note3: hHl lﬁxﬂhabD (Xnﬂ) a > ; ROT nSlQHO. N—ém There is an important connection between the binomial model and sampling. Suppose we are planning to sample n items, and observe whether the selected item has a certain characteristic or not. Before selecting an item think of the population from which the sample is being selected as being thoroughly mixed with respect to the characteristic. Interest is in the random variable, X, the number of items in the sample with the characteristic. Under each of the following situations X is a binomial RV: 1) The population is finite_§£§1each sampled item is replaced back into the population after its possession of the characteristic or not is noted. The population is thoroughly mixed after each item is returned to the population. Here p is the proportion in the population with the characteristic. 2) The population is infinitewandeach sampled item is replaced back into the population after its possession of the characteristic or not is noted. The population is thoroughly mixed after each item is returned to the population. Here p is the probability an item possesses the characteristic. 3) Same as 2) except the item is not replaced. In these three situations the binomial model applies for X. There is a fourth case, of course, and it's a practical case: The population is finite and items are not replaced. The special distribution that models this situation is called the hypergeometric distribution, which leads to our second special discrete random variable. (4.3 in the book). ...
View Full Document

• Spring '08
• Staff
• Probability distribution, Binomial distribution, Discrete probability distribution, Hypergeometric Distribution

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern