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let x be a discrete random variable with positive integer outputs. show that P(x=k) = P(...

let x be a discrete random variable with positive integer outputs.

  1. show that P(x=k) = P( x> k-1)- P( X>k) for any positive integer k.
  2. assume that for all k>=1 we have P(x>k)=q^k. use (a) to show that x is a geometric random variable.
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