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.