If x~Po(6)then find $$P(x=6|5≤ x ≤ 8 )$$ I understand that this is conditional probability but I do not understand how would you solve it?
How does one solve this
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probability
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0Must $x$ take on integer values only? Is your distribution function uniform? – 2017-02-23
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0its a poisson distribution – 2017-02-23
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0OK, I was wondering what the $x\sim Po(6)$ meant. – 2017-02-23
1 Answers
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\begin{align}P(X=6|5 \leq X \leq 8)&=\frac{P(X=6)}{P(5 \leq X \leq 8)}\\&=\frac{P(X=6)}{\sum_{i=5}^8P(X=i)} \\&=\frac{\exp(-\lambda)\frac{\lambda^6}{6!}}{\sum_{i=5}^8\exp(-\lambda)\frac{\lambda^i}{i!}} \\&=\frac{\frac{\lambda^6}{6!}}{\sum_{i=5}^8\frac{\lambda^i}{i!}}\end{align}
where $\lambda = 6$.