The probability that a Poisson random variable $X$ is equal to 4 , where $\lambda = 7$, is
A) $\frac { e ^ { - / } 7 ^ { 4 } } { 4 ! }$

B) $\frac { 7 ! 4 ! } { 11 ! }$

C) $\frac { e ^ { - 4 } 4 ^ { \prime } } { 7 ! }$

D) $\frac { 11 ! } { 7 ! 4 ! }$

Question

The probability that a Poisson random variable $X$ is equal to 4 , where $\lambda = 7$, is
A) $\frac { e ^ { - / } 7 ^ { 4 } } { 4 ! }$

B) $\frac { 7 ! 4 ! } { 11 ! }$

C) $\frac { e ^ { - 4 } 4 ^ { \prime } } { 7 ! }$

D) $\frac { 11 ! } { 7 ! 4 ! }$

Quizplus · Accepted Answer

The probability that a Poisson random variable $X$ is equal to $k$ is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$. For $X=4$ and $\lambda=7$, the correct formula is $\frac{e^{-7} 7^4}{4!}$, which matches choice A.

The Probability That a Poisson Random Variable XXX Is Equal to 4 , Where

The Probability That a Poisson Random Variable $X$ Is Equal to 4 , Where