. Consider continuous random variables, X and Y, with joint density that is f(x,y) = 2 for x, y € [0,1] and where y

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14. Consider continuous random variables, X and Y, with joint density that is f(x,y) = 2 for x, y € [0, 1]
and where y< x. That is, the distribution is uniform over the shaded region in the figure below.
y
Say someone takes a sample of X or Y with equal probability, and then announces that the value is
2/3. What is the probability that the sample is from X?
Transcribed Image Text:14. Consider continuous random variables, X and Y, with joint density that is f(x,y) = 2 for x, y € [0, 1] and where y< x. That is, the distribution is uniform over the shaded region in the figure below. y Say someone takes a sample of X or Y with equal probability, and then announces that the value is 2/3. What is the probability that the sample is from X?
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