# Homework Help: Statistics question (poisson distribution, multivariate )

1. Oct 2, 2011

### XodoX

1. The problem statement, all variables and given/known data

On average, 2.5 telephone calls per minute are received at a corporation's switchboard. Making appropriate assumptions about the distribution ( provide justification ), find the probability that at any given minute there will be more than 2 calls.

2. Relevant equations

No idea.

3. The attempt at a solution

No idea.

1. The problem statement, all variables and given/known data
Let the joint p.d.f of X and Y, f(x,y), be given by

..................x
............1.....2.....3
y..1.....0.3..0.2..0.1
....2 ....0.1..0.1..0.2
(ignore the dots)
a) Determine marginal densities
b) compute the means and variances of X and Y
c) Calculate sigma(?) xy = cov (X,Y) and the correlation coefficient ρ. Are X and Y independent ?
d) Let Z = X+Y. determine k(z)+P(Z=z), z = 2,3,4,5. determine the mean and variance.

2. Relevant equations

good question

3. The attempt at a solution

I don't have one

Well, how do I do this? I do not understand it. If anybody has some insight on either problem, I'd appreciate it.

Last edited: Oct 2, 2011
2. Oct 2, 2011

### XodoX

Got the first one now. About the 2nd one - I THINK I now have b and partly c. but c required the marginal densities, correct ( for the correlation coefficient ) ? I don't know how to do that. The example in the book just tells me ok here it is..without explaining how to get it.