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Probability and conditional distributions

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

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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

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Please see the attached file.

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

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