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Statistics and Probability

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Statistical Software and Poisson Probabilities

STATS-LLFNVZ

For Poisson random variable $X$ with mean $\lambda$, it is known that the statistical software $\large R$ can compute $P(X=x)$ with the command 'ppois($x$,$\lambda$)' and can compute $P(X\leq x)$ with the command dpois($x$,$\lambda$).

Hence, if $X$ is Poisson with mean $3$, $P(X=5)$ can be obtained with the command ppois$(5,3)$ and $P(X\leq5)$ can be obtained with the command dpois$(5,3)$.

How many of the following would result in $P(Y=4)$ for a Poisson random variable $Y$ with mean $5$?

i. dpois$(5,4)$-dpois$(5,3)$

ii. dpois$(5,5)$-dpois$(3,5)$

iii. $[1-$dpois$(3,5)]-[1-$dpois$(4,5)]$

iv. dpois$(4,5)$-ppois$(1,5)$-ppois$(2,5)$-ppois$(3,5)$

v. ppois$(4,5)$-ppois$(3,5)$

A

$0$

B

$1$

C

$2$

D

$3$

E

$4$

F

Cannot be determined