Suppose that X and Y are independent geometric random variables with the same parameter P. Find the value and verify: P ( X = i | X + Y = n ) My initial reaction is that since they are independent and have the same parameter P, that the given is not necessary and the answer would just end up being ( 1 − P ) ( i − 1 ) P but I am pretty sure that I am missing something, can someone help me get started on this proof?

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Suppose that X and Y are independent geometric random variables with the same parameter P. Find the value and verify:  P      (    X    =    i          |        X    +    Y    =    n    )  My initial reaction is that since they are independent and have the same parameter P, that the given is not necessary and the answer would just end up being   (  1  −  P      )          (      i      −      1      )        P but I am pretty sure that I am missing something, can someone help me get started on this proof?

Tania Alvarado · Accepted Answer

Step 1No, the problem is that X and Y satisfy   X  ,  Y  ≥  1. If you know that   X  +  Y  =  4 the value of X can&#039;t be greater than 3.Step 2  P  (  X  =  i         |       X  +  Y  =  n  )  =            P      (      Y      =      n      −      i      ,      X      =      i      )              P      (      X      +      Y      =      n      )      .

Suppose that X and Y are independent geometric random variables with the same parameter P. Find the value and verify: P(X=i|X+Y=n) ?

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