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Question regarding binomial random variable and distribution

  1. Sep 15, 2009 #1
    Hi,

    just started learning probability & need some help in understanding....

    "The binomial random variable X associated with a binomial experiment consisting of n trials is defined as

    X = the number of S's among the n trials.

    Suppose, for example, that n = 3. Then there are 8 possible outcomes for the experiment:

    SSS SSF SFS SFF FSS FSF FFS FFF"

    Why is it that there will be 8 possible outcomes?
     
  2. jcsd
  3. Sep 15, 2009 #2
    You have three trials--each trial has two possible results: S or F. Computing the total number of outcomes of the three trials is a matter of just adding together all of the separate results.

    First trial: 2 results, Second trial: 2 results, Third trial: 2 results

    2*2*2 = 23 = 8 outcomes

    The general formula is: Number of outcomes = pn, where p is the number of possible results of each trial, and n is the number of trials.

    If order doesn't matter, then in your example SSF and FSS would be considered the same outcome since the same number of S and F occur in both. The formula for this is different. Here's a link for more, I'm late for class...

    http://en.wikipedia.org/wiki/Binomial_coefficient
    http://mathworld.wolfram.com/Combination.html
     
  4. Sep 16, 2009 #3
    Thanks very much for the explaination. I understand why there 8 possible outcomes now. thanks again!
     
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