(Solved): (Accuracy) Two random variables X and Y have joint probability density function {41(x2+y2),0, ...
(Accuracy) Two random variables X and Y have joint probability density function {4?1?(x2+y2),0,? if x2+y2?4 and x?0 otherwise ?. (a) Find the marginal densities f1?(x) and f2?(y). (b) Find P(Y<0?X=3?) (c) Find P(X>1?Y=1)
(a) To find the marginal density functions, we need to integrate the joint density function over the appropriate variable.
The marginal density function of X is given by: