Let \( S = [0,2]^3 \) (i.e., the 2 by 2 by 2 cube). Let \( X, Y, Z \) be random variables on \( S \) with joint distribution:\[ f_{XYZ}(x,y,z) = C(\cos \pi x + \sin \pi y + 2)z \]where \( C \) is a constant.a. Find the value of \( C \).b. Find \( f_Z(z) \).c. Find \( \text{Var}(Z) \).d. Find \( f_{XY}(x, y) \).

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Let S = [0,2]3 (i.e. the 2 by 2 by 2 cube). And let X, Y, Z be random variables on S with joint distribution: fxyz(x, y, z) = C(cos x + sinдy + 2)z, where C is a constant.