1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statistics basic question: Probability distrbution

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data
    A random variable X has three, and only three, possible values, 0; 2; 4
    with the following probability distribution:

    Probability:
    Getting a 0 is 0:7

    Getting a 2 is 0:1

    Getting a 4 is 0:2

    Let X1 and X2 be two independent random variables with this distribution.

    (a) Determine the probability distribution for

    X(bar)2 = (X1 + X2)/2
    and use this distribution to determine the expectation and variance of X(bar)2

    (b) Determine the expectation and variance of X and verify that the
    variance of X(bar)2 is one-half the variance of X.


    2. Relevant equations



    3. The attempt at a solution

    X2(bar) = 0 with probability 0.49
    X2(bar) = 1 with probability 0.14
    X2(bar) = 2 with probability 0.29
    X2(bar) = 3 with probability 0.04
    X2(bar) = 4 with probability 0.04

    not sure how to work out the variance?

    Regards as always
    Tam
     
    Last edited: Feb 4, 2012
  2. jcsd
  3. Feb 4, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have the probability distribution of [itex] \bar{X}_2.[/itex] Just apply the _definition_ of variance and the formulas for it that you can find in any relevant book, or on-line if you look.

    RGV
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Statistics basic question: Probability distrbution
Loading...