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Math Help - probability-lower bound on expected number

  1. #1
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    probability-lower bound on expected number

    Hello everyone!

    The problem is:

    Suppose that the probability that a text contains 10 or more instances of the word "president" is 1/5. Provide a lower bound on the expected number of instances of this word
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  2. #2
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    Quote Originally Posted by tanichkap View Post
    Hello everyone!

    The problem is:

    Suppose that the probability that a text contains 10 or more instances of the word "president" is 1/5. Provide a lower bound on the expected number of instances of this word
    The expected number of instances is:

    E(n)=\sum_{r=0}^{\infty} r p(r)

    This is obviously minimised subject to the constraint if p(0)=0.8, p(10)=0.2 and p(r)=0 for all other r.

    So:

    E(n) \ge 2

    and the bound is tight.

    RonL
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