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 jointdistribution:fxyz(x, y, z)= C(соs лx + sinлу + 2)z, where C is a constant.a. Find the value of C.b. Find fz(z)c. Find Var(Z)d. Find fxy(x, y)4

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Answered: Let S = [0,2]3 (i.e. the 2 by 2 by 2…

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 23E

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Question

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(соs лx + sinлу + 2)z, where C is a constant.
a. Find the value of C.
b. Find fz(z)
c. Find Var(Z)
d. Find fxy(x, y)
4

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Step 1: Write the given information.

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Step 2: Find the value of C.

Step 3: Find f(Z).

Step 4: Find Var(Z).

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