Find the standard deviation of the Poisson random variable. Round to three decimal places.
-In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 4.800$. Let $\mathrm { X }$ denote the number of burglaries in the town in a randomly selected week. Find the standard deviation of X.
A)$23.040$
B) $2.191$
C) $4.800$
D) $2.400$

Question

Find the standard deviation of the Poisson random variable. Round to three decimal places.
-In one town, the number of burglaries in a week has a Poisson distribution with parameter $\lambda = 4.800$. Let $\mathrm { X }$ denote the number of burglaries in the town in a randomly selected week. Find the standard deviation of X.  
A)$23.040$
B) $2.191$
C) $4.800$
D) $2.400$

Quizplus · Accepted Answer

The standard deviation of a Poisson random variable is the square root of its parameter $\lambda$. Therefore, $\sqrt{4.800} \approx 2.191$.

Find the Standard Deviation of the Poisson Random Variable λ=4.800\lambda = 4.800λ=4.800

Find the Standard Deviation of the Poisson Random Variable $\lambda = 4.800$