3. Continuous random variables X and Y have ranges 0 ≤ X ≤ 2 and 1 ≤ Y ≤ 3. Suppose that X and Y have joint probability density function fx,y(x, y) = 3 64 (x + y²). (a) Find a formula for the conditional density fx|x=y(x, y). (b) Find a formula for the conditional density fyx=x(x, y).
3. Continuous random variables X and Y have ranges 0 ≤ X ≤ 2 and 1 ≤ Y ≤ 3. Suppose that X and Y have joint probability density function fx,y(x, y) = 3 64 (x + y²). (a) Find a formula for the conditional density fx|x=y(x, y). (b) Find a formula for the conditional density fyx=x(x, y).
A First Course in Probability (10th Edition)
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Transcribed Image Text:3. Continuous random variables X and Y have ranges 0 ≤ X ≤ 2 and 1 ≤ Y ≤ 3.
Suppose that X and Y have joint probability density function
fx,y(x, y) = x+y²).
3
64
(a) Find a formula for the conditional density fx|x=y(x, y).
(b) Find a formula for the conditional density fy|x=x(x, y).
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