Question

The number of visits to a website follows a poisson distribution with an average of 90 per hour.

What is the probability that there will be at least 2 visits in one minute?

What is the probability that the time between successive visits will be less than 0.5 minutes?

Answer 1

1)

expected number of visits in 1 minute =90/60 =1.5

probability that there will be at least 2 visits in one minute =P(X>=2)=1-P(X<=1)

=1-e^-1.5*1.5⁰/0!-e^-1.5*1.5¹/1! =1-0.557825 =0.442175

2) probability that the time between successive visits will be less than 0.5 minutes

=1-e^-1.5*0.5 =0.527633