A random variable Y is said to be Poisson random variable if Y takes value 0,1,2,3... with λ as a parameter.
A Poisson random variable is used to approximate a binomial if the value of n is large and p is very small.
and λ = np
1. The no. of an accident occurring on a highway each day is poisson random variable with parameter 3.
What is the probability that no accident occurred?
They are clearly saying " no accident " which means i=0
So using the above formula :
p(i=0) = (e-3 (3)0 ) / 0 !
= e-3 or
remember 0! =1