1. The discrete random variables Xo, X, and X have the following joint distribution: For Xo...

  

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1. The discrete random variables Xo, X₁, and X₂ have the following joint distribution: For Xo = 2: X₂ 2 4 6 1 X₁ 3 5 30 60 60 20 T 60 60 20 For Xo = 5: X₂ 2 4 6 1 18 1 18 X1 3 2010 5 36 36 36 36 where the left table is the joint pmf values of the random vector X (Xo, X1, X₂) for Xo = 2, and the right table is the joint pmf values of X for Xo = 5. Answer the following questions. All logarithms are in base 2. If you choose to write a script to compute the answers, make sure to attach your code, but also write the answers. If you choose to hand-write your answer justify all your solutions. 1c) Which, if any, of the pairs (X₁, X2), (Xo, X2), and (Xo, X₁) are inde- pendent? Justify your answer. 1d) What is the conditional distribution of the random vector (X1, X2) given Xo = 2? Repeat for given Xo = 5. le) Are the random variables X₁ and X2 conditionally independent given Xo = 2? = 2? Repeat for given Xo = 5. 1f) What is the conditional distribution of X₁ given Xo = 5 and X₂ = 2? 1. The discrete random variables Xo, X₁, and X₂ have the following joint distribution: For Xo = 2: X₂ 2 4 6 1 X₁ 3 5 30 60 60 20 T 60 60 20 For Xo = 5: X₂ 2 4 6 1 18 1 18 X1 3 2010 5 36 36 36 36 where the left table is the joint pmf values of the random vector X (Xo, X1, X₂) for Xo = 2, and the right table is the joint pmf values of X for Xo = 5. Answer the following questions. All logarithms are in base 2. If you choose to write a script to compute the answers, make sure to attach your code, but also write the answers. If you choose to hand-write your answer justify all your solutions. 1c) Which, if any, of the pairs (X₁, X2), (Xo, X2), and (Xo, X₁) are inde- pendent? Justify your answer. 1d) What is the conditional distribution of the random vector (X1, X2) given Xo = 2? Repeat for given Xo = 5. le) Are the random variables X₁ and X2 conditionally independent given Xo = 2? = 2? Repeat for given Xo = 5. 1f) What is the conditional distribution of X₁ given Xo = 5 and X₂ = 2?