Unformatted text preview: U and V independent random variables? Why or why not? 4. Let the joint pdf of ( X,Y ) be f ( x,y ) = 1 on { < x < 1 , x < y < x + 1 } and zero otherwise. Find the following: (a) The marginal distribution of X , E ( X ) and V ar ( X ). (b) The marginal distribution of Y , E ( Y ) and V ar ( Y ). (c) E ( XY ), Cov ( X,Y ), and ρ XY . Are X and Y independent? Why or why not? 5. Devore (7e) Text: 5.18 (p. 196) 6. Let X be the mean of a random sample of size n = 10 from a distribution with pdf f ( x ) = 6 x (1x ) , < x < 1. (a) Find the mean of X . (b) Find the variance of X . 7. Devore (7e) Text: 5.52 (p. 218) 8. Devore (7e) Text: 5.60 (p. 222) 9. Let X be the mean of a random sample of size n = 36 from an exponential distribution with mean 4. (a) Find P (3 . 1 < X 1 < 4 . 6). (b) Approximate P (3 . 1 < X < 4 . 6). 10. Devore (7e) Text: 5.66 (p. 222)...
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 Spring '05
 STAFF
 Probability distribution, Probability theory, independent random variables, joint probability distributions, Basic Engineering Probability

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