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(Solved): Problem 9. The joint density of random variables \( X \) and \( Y \) is \[ f_{X, Y}(x, y)=\left\{\ ...
Problem 9. The joint density of random variables \( X \) and \( Y \) is \[ f_{X, Y}(x, y)=\left\{\begin{array}{ll} c\left(x^{2}+y^{2}\right) e^{-x} & 0 \leq x<\infty,-x \leq y \leq x \\ 0 & \text { otherwise } \end{array}\right. \] Find \( \mathrm{P}(Y \leq y \mid X=x) \)
Expert Answer
from the given probability density function we find the value of c where ?=infinite ??f(X,Y)dydy=1 ?0. ??xxC(x2+y2)e?xdydx=1 ?0C