# random variables

Prove the following:

a) Fxy(a,b) is non-decreasing (in a and b).

b) lim a->inf Fxy(a,b) = Fy(b)

c) Jointly continuous random variables X and Y are independent if and only if

fxy(x,y) = fx(x)*fy(y)

fxy(x,y) is the joint probability density function.

Fxy(a,b) is the joint cumulative distribution function where x y (this is not x*y) are random variables.

https://brainmass.com/statistics/probability/probability-random-variables-427323

#### Solution Summary

Probability of random variables is articulated.

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