2- [30P] Consider two random variables X and Y with joint probability mass function (pmf) given in table below. a. Find P (X?2, Y?4) [5P]. b. Find the marginal pmfs of X and Y. [10P] c. Find P(Y=2|X=1) [5P]. d. Are X and Y independent? [10P] | | Y = 2 | Y = 4 | Y = 6 | | :--- | :---: | :---: | :---: | | X = 1 | 1/12 | 1/24 | 1/24 | | X = 3 | 1/6 | 1/12 | 1/8 | | X = 5 | 1/4 | 1/8 | 1/12 |
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Identify the joint probability mass function (pmf) for X and Y. Show more…
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The bivariate X and Y has the probability mass function (PMF) given by: P_{XY}(x, y) = { k x = 0, 1, 2 & y = 1, 2, 3 0 Otherwise a. Compute the value of the constant k and plot the joint PMF b. Find the marginal PMFs of the random variables X and Y c. Calculate the following: i. P[X = 0 | Y = 1] ii. P[X >= 1 | Y > 1] iii. P[{0 <= X < 2} cap {1 < Y < 3}] iv. The correlation coefficient ho_{XY}
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