Sheldon Ross 10: Exercise 3.02

Question: Let X1 and X2 be independent geometric random variables having the same parameter p. Guess the value of P{X1=i | X1+X2=n}


Analytical Solution: This can be modelled by using the principles of conditioning on the probability. The equation would become the following,

P{ X1=i | X1+X2=n} =  P{X1=i, X2=n-i | X1+X2=n}P{X1+X2=n}

pi(1-p)n-i p1(1-p)n-i-1NegativeBinomial[n,p]

= pi(1-p)n-i p1(1-p)n-i-1nC1 p(1-p)n-21n-1

NegativeBinomial[n,p] is the mathematica function and it requires two parameters i.e., n and p.


End of the tiny post 😐


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