Question: Semester Two Practice Examinations, 2022 Question 1. [10 marks] Suppose X and Y have the joint probability mass function x 0 1 2 0

Semester Two Practice Examinations, 2022 Question 1. [10 marks] Suppose X and Y have the joint probability mass function x 0 1 2 0 CO 0.175 0.105 1 0.18 0.075 C1 where CO and C are real numbers such that the marginal probability mass function of Y is Y 0 1 P(Y=y) 0.7 0.3 (a) Determine the values co and c. STAT2201 [2 marks] (b) Determine the expectation and variance of X. [4 marks] (c) Are the events {X = 0} and {Y = 1} are independent. Justify your answer. [2 marks] (d) Determine E(4X+2Y) [2 marks]

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