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Unformatted text preview: Î» ). 3 Let X be a continuous random variable with expectation Î¼ and probability density function f . Prove that Z âˆžâˆž ( xÎ¼ ) 2 f ( x ) d x = E ( X 2 )Î¼ 2 . 4 Let X âˆ¼ uniform[0 , 4] and put Y = âˆš X . Find the probability density function of Y . Hence ï¬nd the expectation and variance of Y . 5 Let Z be a standard normal random variable. Find (a) P ( Z < 2 . 55) (b) P ( Z > . 10) (c) P ( Z <1 . 41) (d) P ( Z < e) (e) P (2 â‰¤ Z â‰¤ 1). 6 Let Z âˆ¼ N (0 , 1). Find x such that P ( Z < x ) = 0 . 875. Give the answer to three signiï¬cant ï¬gures. 1 7 (Feedback) Let X âˆ¼ N (4 , 16). Find (a) P ( X < 6) (b) P ( X > 0) (c) P (2 â‰¤ X â‰¤ 3) (d) P ( X â‰¤ 1 . 53). 8 Let X âˆ¼ N (10 , 25). Find x such that P ( X < x ) = 1 / 10. Give the answer to three signiï¬cant ï¬gures. 2...
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 Spring '12
 R.A.Bailey
 Statistics, Normal Distribution, Variance, Probability theory, probability density function, UNIVERSITY OF LONDON

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