Sunday, 22 July 2012

Repeated Albhabets

Consider a 36 letter word. Find the expected number of the alphabets that would be repeated?

1 comment:

  1. Let the letters a to z be a1,a2,....a26
    Now, let a1=1 if letter 'a' is repeated ow 0
    Similarly for a2 to a26
    Now,
    Let N=number of alphabets repeated = a1+a2+...+a26
    Then,
    E(N)= E(a1)+E(a2)+....+E(a26)
    Now,
    E(a1) = 1*P(a1=1) +0*P(a1=0)
    E(a1) = P(a1= 1) = 1-P(a1=0)
    Now,
    P(a1=0) = letter 'a' doesn't appear on the 36 word or appears only once
    P(a1=0) = [36C0*(1/26)^0*(25/26)^36] +
    [36C1*(1/26)^1*(25/26)^35]

    Thus, we can find the expected alphabets that would be repeated.

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