Suppose that the random variables X, Y , and Z have the following joint probability distribution.

Determine the following:

(a) P(X = 2) 

(b) P(X = 1, Y = 2)

(c) P(Z <1.5) 

(d) P(X = 1 or Z = 2)

(e) E(X ) 

(f) P(X = 1|Y = 1)

(g) P(X = 1, Y = 1| Z = 2) 

(h) P(X = 1|Y = 1, Z = 2)

(i) Conditional probability distribution of X given that Y = 1 and Z = 2

f(x, y, z) 1 1 0.05 1 1 2 0.10 1 2 1 0.15 1 2 0.20 1 0.20 2 1 0.15 2 1 0.10 2 2 0.05