(a) Just looking at the table of joint probabilities and providing all calculations in mind, find P(X₁ = 3|X₂ = 0).

(b) Just looking at the table of joint probabilities and providing all calculations in mind, write the conditional distribution of X₂ given X₁ = 0; the conditional distribution of X₁ given X₂ = 3. 

(c) Guess whether it is true that P(X₂ = 1|X₁ = 1) = P(X₂ = 1), and that P(X₁ = 1|X₂ = 1) = P(X₁ = 1). Compute these probabilities and check your guess.