Problem 1 Let X, Y and Z be three jointly continuous random variables with joint PDF x + y 0 < x, y, z < 1 fxxz (x, Y, z) = otherwise 1. Find the joint PDF of X and Y. 2. Find the marginal PDF of X. 3. Find the conditional PDF of fxy|z (x, y|z) using fxyz (x, Y, z) fz(2) fxy|z (x, y|2) = 4. Are X and Y independent of Z?

Problem 1 Let X, Y and Z be three jointly continuous random variables with joint PDF x + y 0 < x, y, z < 1 fxxz (x, Y, z) = otherwise 1. Find the joint PDF of X and Y. 2. Find the marginal PDF of X. 3. Find the conditional PDF of fxy|z (x, y|z) using fxyz (x, Y, z) fz(2) fxy|z (x, y|2) = 4. Are X and Y independent of Z?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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