Let X and Y be jointly continuous with density f X,Y . Let (R, ) be the
Question:
Let X and Y be jointly continuous with density fX,Y. Let (R, Θ) be the polar coordinates of (X, Y).
(a) Give a general expression for the joint density of R and Θ.
(b) Suppose X and Y are independent with common density function f(x) = 2x, for 0 < x < 1. Use your result to find the probability that (X, Y) lies inside the circle of radius one centered at the origin.
Step by Step Answer:
a We have r x 2 y 2 and tan 1 yx The inverse transfo...View the full answer
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