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Binomial trials

  1. Nov 3, 2004 #1
    In a series of three binomial trials with p=.4, a random variable, X, is assigned to the outcomes to form a base 2 number, with 1 associated with success(S), and 0 associated with failure(F). For example, SFS->101=5.

    A) Find the expected value of X, E[X].
    (Answer 2.80)

    B) Find the expected value of X if P=.5
    (Answer 3.5)
     
  2. jcsd
  3. Nov 9, 2004 #2
    What have u done so far?

    -- AI
     
  4. Dec 4, 2004 #3
    I think you mean 3 bernoulli trials and not binomial trials. Remember bernoulli trials have just 2 outcomes (1 and 0 in your question).
    Since you know the 3 digit number (from the SFS or other combinations) just use definition of Expectation.
    E[X] = Summation (x*P(x))
    In your case the x would be 1*2^n and 0*2^n(which is 0 so can ignore)...n is the power corresponding to the placing of the number.
    As for a number at the unit's place, you would have 1*2^0.
    For Bernoulli the expectation is just p and then use the definition to obtain the result.

    Hope this helps.
     
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