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AP EAMCET2012MathematicsProbability

Suppose X follows a binomial distribution with parameters n and p , where 0 < p < 1 . If P(X=r) P(X=n-r) is independent of n for every r , then p is equal to

Options

  1. A1 2
  2. B1 3
  3. C1 4
  4. D1 8

Correct answer

A. 1 2

Step-by-step solution

Given P(X=r)= ^n C_r p^r q^ n-r aligned P(X=r) P(X=n-r) & = ^n C_r p^r q^ n-r ^n C_ n-r p^ n-r q^r & = ( q p )^ n-2 r aligned For independent of n, q n =1 array ll & q=p & p+q=1 & 2 p=1 p= 1 2 array

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