Solving for the CDF of the Geometric Probability DistributionFind the CDF of the Geometric distribution whose PMF is defined as P ( X = k ) = ( 1 − p ) k − 1 p where X is the number of trials up to and including the first success.

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Solving for the CDF of the Geometric Probability DistributionFind the CDF of the Geometric distribution whose PMF is defined as   P  (  X  =  k  )  =  (  1  −  p      )          k      −      1        p where X is the number of trials up to and including the first success.

DoryErrofbi · Accepted Answer

Explanation:The CDF is defined as   F  (  k  )  =  P  (  X  ≤  k  )  =      ∑                  k        ′            =      1        k    P  (  X  =      k    ′    )  =      ∑                  k        ′            =      1        k    p  (  1  −  p      )                  k        ′            −      1        =  1  −  (  1  −  p      )    k       , using a finite geometric sum .

Find the CDF of the Geometric distribution whose PMF is defined as P(X=k)=(1-p)^{k-1}p

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