1. ## Probability question

Hi I'm new here!

I was looking through an old exam that I totally bombed thinking that I should be able to do it now, but I'm turning up just as clueless. Not knowing the answer is realy bugging me:

"A particular website receives on average one hit per hour on a weekday afternoon. Let X denote the number of hits to be registered between noon and 3PM next Thursday.

a) Find Var(X)
b) Find P(X >=2)
c) Let Y denote the number of hits to be registered between 3PM and 6PM next Thursday. Find Var(X + Y)
d) Find E((X+Y)^2)

Any help would be greatly appreciated!

2. Hi Sushi2008,

It seems reasonable to assume the number of hits per time period has a Poisson distribution, so X has a Poisson distribution with mean 3. This is also the variance.

To find P(X >= 2), use P(X >= 2) = 1 - P(X=0) - P(X=1) and the formula for the pdf of a Poisson distribution.

If Y also has a Poisson distribution with mean 3, then X+Y has a Poisson distribution with mean 6 (and variance 6).

To find E[(X+Y)^2], use var(X+Y) = E[(X+Y)^2] + [E(X+Y)]^2.

Hope this helps,
jw

3. Originally Posted by sushi2008
Hi I'm new here!

I was looking through an old exam that I totally bombed thinking that I should be able to do it now, but I'm turning up just as clueless. Not knowing the answer is realy bugging me:

"A particular website receives on average one hit per hour on a weekday afternoon. Let X denote the number of hits to be registered between noon and 3PM next Thursday.

b) Find P(X >=2)

Any help would be greatly appreciated!
For the evaluation of Sushi's comment to check your work, go here:

Poisson Distribution

n = 3, p = 1, k = 1 since we want >= 2.