Question

# 1. Suppose the number of junk emails you received per day has a Poisson distribution with...

1. Suppose the number of junk emails you received per day has a Poisson distribution with an average of five per day.

a) What is the probability that you receive 3 junk emails per day?

b) What is the probability that you receive at least 1 junk email per day?

c) What is the probability that you receive at most 3 junk emails per day?

d) What is the likelihood of receiving between 3 and 6 junk emails per day?

a)

 this is Poisson distribution with parameter λ=5

probability that you receive 3 junk emails per day =P(X=3) =e-5*53/3! =0.1404

b)

probability that you receive at least 1 junk email per day =P(X>=1)=1-P(X=0) =1-e-5*50/0!

=1-0.0067 =0.9933

c(

probability that you receive at most 3 junk emails per day =P(X<=3)

=P(X=0)+P(X=1)+P(X=2)+P(X=3)

=e-5*50/0! +e-5*51/1! +e-5*52/2! +e-5*53/3!

=0.0067+0.0337+0.0842+0.1404=0.2650

d)

P(3<=X<=6) =P(X=3)+P(X=4)+P(X=5)+P(X=6)

=e-5*53/3!+e-5*54/4!+e-5*55/5!+e-5*56/6! =0.6375