# Probability and conditional distributions

Probability and conditional distributions. See attached file for full problem description.

© BrainMass Inc. brainmass.com December 15, 2020, 1:10 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/probability-conditional-distributions-100579

#### Solution Preview

Please see the attached file.

I think you know the basic integration steps. So I am avoiding the integration steps

Solution

9. a. Given , 0 < x < y , 0 < y <1

The given range can be combined and written in the form 0 < x < y < 1.

To find the marginal density of X (or Y) , integrate f (x,y) w.r.t Y (or X). (Note that range of integration should be taken from the combined range whenever x and y simultaneously included in the integration)

The marginal densities is given by,

= 2 (1-x) , 0 < x < 1

= 2y , 0 < y < 1

The ...

#### Solution Summary

Solution reveals some relationships between the binomial and Poisson distribution. Also it includes method for finding the correlation coefficient between two random variables