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Statistics - Expected Value

  1. Nov 9, 2011 #1
    Hi,

    I have to work with Expected Values and I am extremely confused over the following:

    In the part of my book that teaches me about Probability Distribution, in order to calculate the Expected Value I have to:

    Lets say we toss a coin twice. We can get 0 Heads, 1 Heads or 2 Heads

    I then draw a probability distribution table and the expected value is the sum of the product of the number of heads and their respective probabilities.

    When I get to the part that I learn about Binomial Distributions, in order to get the expected value all I have to do is multiply n by p whereas n is the number of tries and p the probability of success.

    What is the difference between the two methods? When should I use each?

    Thanks!
     
    Last edited: Nov 9, 2011
  2. jcsd
  3. Nov 9, 2011 #2

    danago

    User Avatar
    Gold Member

    The equation for the EV of a binomial distribution is derived from the exact same procedure the you have described (sum the product of the outcomes with their respective probabilities) i.e. if X~Bin(n,p), then:

    [tex]E(X)=\sum_{x=0}^{n}xP(X=x)[/tex]

    So for any n, you could in fact just draw up a table of outcomes and then continue with how you originally solved it, however that will be a lot more work for large n. It is probably a good exercise to try and actually derive the equation E(X)=np from the equation i have posted above, so you can see for yourself that they are identical.

    EDIT:
    Have a look at this:

    http://amath.colorado.edu/courses/4570/2007fall/HandOuts/binexp.pdf [Broken]

    It will show you the derivation. Also keep in mind that this only works for binomial random variables.
     
    Last edited by a moderator: May 5, 2017
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