Unformatted text preview: (c) Evaluate P{Y>X}. 4. The joint density function of X and Y is (a) Are X and Y independent? Give a reason for your answer. (b) Find a formula for the density function of X. (c) Find a formula for the density function of Y. (d) Find a formula for the joint cumulative distribution function. (e) Evaluate E[Y]. (f) Evaluate P{X+Y < 1}. 5. Let X and Y be continuous random variables with joint probability density function (a) . )  ( Find Y  X y x f (b) ). Y  E(X Find y = 6. Urn 1 contains 2 white and 2 black balls, while urn 2 contains 1 white and 2 black balls. One ball is randomly selected from urn 1 and put into urn 2. Then two balls are randomly selected from urn 2. Let the random variable X be the number of white balls selected from urn 2. Compute E[X]. otherwise , 2 y , 1 x , xy y) f(x, < < < < = otherwise , 1 y , 1 x , y x y) f(x, < < < < + =...
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 Fall '07
 ENGQUIST
 Math, Statistics, Normal Distribution, Probability, Probability theory, probability density function, density function, Cumulative distribution function

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