The random variable X, Y and Z have the following joint probability distribution: X 1 1 1 1 2 2 y 1 1 2 2 1 1 Z 1 2 1 2 1 2 f(x,y,z) 0.05 0.10 0.15 0.20 0.20 0.15 Determine the following: 1. P(X=1, Y=2) 2. P(Z<1.5) 3. P(X=1 or Z=2) 4. Conditional probability distribution of X given that Y=1 and Z = 2.

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