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MATH3334 Exam 3

# MATH3334 Exam 3 - (c Evaluate P{Y>X 4 The joint density...

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Name:_______________ Practice Exam 3 Math 3334 Fall, 2007 1. Let X be an exponential random variable with λ =1. Find the density function of Y = X 2 . 2. The scores on an achievement test given to 100,000 students annually are normally distributed with mean 500 and standard deviation 100. What should the score of a student be to place him among the top 10% of all students? You may use Tables 1 and 2 from the Appendix of the textbook. 3. Suppose a coin has probability 1/3 of landing heads and probability 2/3 of landing tails. Suppose a die has probability i/21 that i spots will show on the upturned face when the die is rolled, i = 1,2,...,6. An experiment consists of flipping the coin and then rolling the die. Let X be the number of heads showing on the coin and let Y be the number showing on the die. (a) Write the joint probability mass function of X and Y in tabular form. (b) Evaluate E[XY] and E[X+Y].
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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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