elemprob-fall2010-page18

elemprob-fall2010-page18 - ± 5 2 ²± 3 2 ² ± 8 4 ² If...

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

View Full Document Right Arrow Icon
we are looking at the number of successes in 365 “trials.” In other words, we are looking at a binomial. The above proposition says that this can be approximated very well by a Poisson. If instead of days, we look at minutes, the approximation is even better. 7 Hypergeometric distributions Suppose we have an urn with 5 red marbles and 3 green marbles. We pick 4 marbles without replacement and ask, what is the probability we have 2 red marbles and 2 green marbles? We could also pick 4 marbles with replacement and get a different answer. There are 8 4 ways of choosing 4 marbles out of 8 total, all equally likely. There are 5 2 ways of choosing 2 red marbles out of the 5 red ones and
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ± 5 2 ²± 3 2 ² ± 8 4 ² . If there are m of one type, n of another, and we want N total to be chosen, with k of hte first type, the probability becomes ± m k ²± n N-k ² ± m + n N ² . A random variable with these probabilities ( m,n,N are parameters, k the possible values) is said to have a hypergeometric distribution. An example. What is the probability that in a poker hand (5 cards out of 52) we get exactly 4 of a kind? Answer: The probability of 4 aces and 1 king is ± 4 4 ²± 4 1 ² . ± 52 5 ² . The probability of 4 jacks and one 3 is the same. There are 13 ways to pick the 18...
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