Question

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?

Answer 1

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