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- Round numbers to three decimal places (when needed). 0 Clearly mark which question/part you are answering. - Unless noted otherwise, different parts shall be treated independently. 0 Show the steps of calculation/argument. We will award maximum partial credit possible in the case of an incomplete response. - List/state/make any assumptions, if needed. The joint probability distribution of X and Y is partially shown in the table below. (i 0 0.01 0.1 0.2 [V 4.. IV [(1 w 0.5 0.2 In addition you know the conditional probability P(Y = 4[X = 1) = 0.5 1. (3 points) Complete the table (show your math and your reasoning below) 2. (2 points) Compute the expected value of X (show your math) 3. (3 points) Compute the standard deviation ofX (show your math) 4. (2 points) Compute P(X = 2 | Y = 2) (show your math) 5. (2 points) Are X and Y independent? Explain how you get the result