Finding the Probability of a multiple using geometric distributionLet X be a geometric distribution with parameter p = 1 9 i.e. P ( X = k ) = 8 9 ( k − 1 ) 9 for k ∈ { 1 , 2 , 3 , . . . }.Let A be the event that X is a multiple of four. What is the value of P(A)? How do I find k in this instance?

Question

Finding the Probability of a multiple using geometric distributionLet X be a geometric distribution with parameter   p  =      1    9   i.e.   P  (  X  =  k  )  =                    8        9                    (        k        −        1        )              9   for   k  ∈  {  1  ,  2  ,  3  ,  .  .  .  }.Let A be the event that X is a multiple of four. What is the value of P(A)? How do I find k in this instance?

Phillip Fletcher · Accepted Answer

Explanation:  P  (  X  ∈  A  )  =      ∑          k      =      0              +      ∞        P  (  X  =  4  k  ) which gives you a geometric series to compute.

Let X be a geometric distribution with parameter p=1/9 i.e. P(X=k)=(8/9)^{k-1}/9 for k in {1, 2, 3, . . .}

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