Question: Probability QUESTION 3 (20 marks) Suppose that a fair die is rolled n times independently. For each i = 1,. . . ,6, let X;

Probability

QUESTION 3 (20 marks) Suppose that a fair die is rolled n times independently. For each i = 1,. . . ,6, let X; denote the number of times 2' appears. (a) (2 marks) Find the probability mass function of X2. (b) (2 marks) Find the joint probability mass function of (X2, X4). (c) (2 marks) Find the conditional probability mass function of X2 given that X4 = E (0 S E S n). (d) (4 marks) Find the probability mass function of X2 + X4. (e) (10 marks) Find Cov(X2,X4)

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