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Statistics and Probability

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Moderate

Identifying Poisson Random Variables

STATS-0XEFEE

How many of the following experiments must be Poisson random variables?

i. An experiment which records the number of light bulbs that burn out within $48$ hours from a box filled with $20$ light bulbs where the average lifetime of a lightbulb is $60$ hours.

ii. An experiment which records the time it takes $50$ people to cross an intersection where people cross the intersection at an average rate of $10$ per minute.

iii. An experiment with probability mass function given by $p(x)=\dfrac{5^x}{x!}(.006738)$ for $x=0,1,2,\ldots$.

iv. An experiment which records the number of customers that visit a restaurant in a day where customers enter the store at an average rate of $10$ per hour.

v. An experiment which records the number of views a YouTube video receives in a month where the video receives views at an average rate of $100$ per day.

A

$1$

B

$2$

C

$3$

D

$4$

E

$5$

F

Cannot be determined