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Conditional Distribution: Binomial | Poisson Process | GATE ST 2025 | Problem-41 | RitwikMath
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YouTubeRitwikMath
Conditional Distribution: Binomial | Poisson Process | GATE ST 2025 | Problem-41 | RitwikMath
Given the joint probability mass function: [ P(X=m, Y=n) = frac{lambda^n e^{-lambda}}{2^n m! (n-m)!}, quad m=0,1,dots,n; , n=0,1,2,dots ] Key marginal and conditional distributions: **Marginal of (X)**: [ P(X=m) = sum_{n=m}^infty P(X=m,Y=n) = e^{-frac{lambda}{2}} frac{(frac{lambda}{2})^m}{m!} quad Rightarrow quad X sim text{Poisson}left(frac ...
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