Lecture8 - Important Distributions Discrete Uniform...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Important Distributions 10/20/2005
Image of page 1

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

View Full Document Right Arrow Icon
Discrete Uniform Distribution All outcomes of an experiment are equally likely. If X is a random variable which represents the outcome of an ex- periment of this type, then we say that X is uniformly distributed. If the sample space S is of size n , where 0 < n < , then the distribution function m ( ω ) is defined to be 1 /n for all ω S . 1
Image of page 2
Binomial Distribution The distribution of the random variable which counts the number of heads which occur when a coin is tossed n times, assuming that on any one toss, the probability that a head occurs is p . The distribution function is given by the formula b ( n, p, k ) = n k p k q n - k , where q = 1 - p . 2
Image of page 3

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

View Full Document Right Arrow Icon
Exercise A die is rolled until the first time T that a six turns up. 1. What is the probability distribution for T ? 2. Find P ( T > 3) . 3. Find P ( T > 6 | T > 3) . 3
Image of page 4
Geometric Distribution Consider a Bernoulli trials process continued for an infinite number of trials; for example, a coin tossed an infinite sequence of times. Let T be the number of trials up to and including the first success.
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the 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