Question: The joint distribution of the continuous random variables X, Y, and Z is constant over the region x 2 + y 2 1, 0

The joint distribution of the continuous random variables X, Y, and Z is constant over the region x2 + y2 ≤ 1, 0< z < 4. Determine the following:

(a) P(X2 + Y2 ≤ 0.5) 

(b) P(X2 + Y2 ≤ 0.5, Z <2)

(c) Joint conditional probability density function of X and Y given that Z = 1

(d) Marginal probability density function of X

(e) Conditional mean of Z given that X = 0 and Y = 0

(f) Conditional mean of Z given that X = x and Y = y

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