Question

Suppose that $x$ is the number of cars per minute that pass through a certain intersection, and that $x$ has the Poisson distribution. If the mean of $x$ is equal to $9\text{cars}$, what is the variance of $x$?

• A. $9^2\text{cars}$
• B. $9{\text{cars}}^2$

Answer 1

The correct option is B

$9{\text{cars}}^2$

Explanation for the correct option:

Determine the variance.

Recall that the mean of a Poisson distribution is numerically equal to its variance. It is given that $x$, the number of cars per minute that pass through a certain intersection has the Poisson distribution with the mean of $9\text{cars}$. Thus, its variance will be $9{\text{cars}}^2$.

$9{\text{cars}}^2$, matches the variance calculated in the first step.

Thus, option B is correct.

Explanation for the incorrect option:

$9^2\text{cars}$ has the wrong units and cannot represent the variance of the number of cars $x$. The variance must have units equivalent to the square of the units of the random variable, namely, ${\text{cars}}^2$.

Thus option A is incorrect.

Thus, option B is the correct option.