Probability X is odd in a geometric distributionLet X be a Geometric distribution with parameter p = 1 10 .

Question

Probability X is odd in a geometric distributionLet X be a Geometric distribution with parameter   p  =      1    10  .

tiltat9h · Accepted Answer

Step 1  P  (  X is odd  )  =  P  (  X  =  1  )  +  P  (  X  =  3  )  +  P  (  X  =  5  )  +  …The pmf of a geometric distribution is       q          k      −      1        p.Step 2So   P  (  X is odd  )  =      q          0        p  +      q          2        p  +      q          4        p  +  …  =  p      ∑          k      =      0              ∞            q          2      k        =      p          1      −              q                  2

glyperezrl · Accepted Answer

Step 1Imagine that if X is odd then Alphonse wins the game, while if X is even then Beti wins the game. It is clear that with probability 1 one of Alphonse or Beti wins. Let p be the probability A wins.Step 2If A fails to win on the first trial, then the roles of A and B are reversed, and B has probability p of winning. It follows that   p  +      9    10    p  =  1..Solve for p.

Let X be a Geometric distribution with parameter p=1/10.

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