The random variables X and Y have the marginal (in red) and joint probability distributions as...
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The random variables X and Y have the marginal (in red) and joint probability distributions as shown in the table below. The probabilities a, b, c, d, e, f, and g are unknown in the table. Y 1 2 3 fx (x) 0 0.02 0.03 0.05 a 1 f X 2 0.06 d e 0.1 g 0.2 0.3 3 0.08 0.12 0.2 C a) Find a, b, c, d, e, f and g. b) What is the probability that Y is equal to 2 knowing that X is 0? c) What is the probability that X is equal to 0 knowing that Y is not 2? d) Find the correlation between X and Y. Are they independent? Justify. fy(y) 0.2 b 0.5 1 [7 marks] [3 marks] [3 marks] [5 marks] The random variables X and Y have the marginal (in red) and joint probability distributions as shown in the table below. The probabilities a, b, c, d, e, f, and g are unknown in the table. Y 1 2 3 fx (x) 0 0.02 0.03 0.05 a 1 f X 2 0.06 d e 0.1 g 0.2 0.3 3 0.08 0.12 0.2 C a) Find a, b, c, d, e, f and g. b) What is the probability that Y is equal to 2 knowing that X is 0? c) What is the probability that X is equal to 0 knowing that Y is not 2? d) Find the correlation between X and Y. Are they independent? Justify. fy(y) 0.2 b 0.5 1 [7 marks] [3 marks] [3 marks] [5 marks]
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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