Probability of events for a Poisson distribution
An event can occur 0, 1, 2, … times in an interval. The average number of events in an interval is designated $\lambda$ (lambda). Lambda is the event rate, also called the rate parameter. The probability of observing $k$ events in an interval is given by the equation
where
- is the average number of events per interval
- e is the number 2.71828... (Euler's number) the base of the natural logarithms
- k takes values 0, 1, 2, …
- k! = k × (k − 1) × (k − 2) × … × 2 × 1 is the factorial of k.
here $k=0 , \lambda =\frac{45\times 20}{60} =15$ (avg no of events in 45 minutes =15, since rate is 20 request per hr )
so probability of no request in 45 min is,
$P(0)=\frac{15^0 e^{-15}}{0!}=e^{-15}$
hence ans is A