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