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Unformatted text preview: λ ). 3 Let X be a continuous random variable with expectation μ and probability density function f . Prove that Z ∞∞ ( xμ ) 2 f ( x ) d x = E ( X 2 )μ 2 . 4 Let X ∼ uniform[0 , 4] and put Y = √ X . Find the probability density function of Y . Hence ﬁnd 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 ≤ Z ≤ 1). 6 Let Z ∼ N (0 , 1). Find x such that P ( Z < x ) = 0 . 875. Give the answer to three signiﬁcant ﬁgures. 1 7 (Feedback) Let X ∼ N (4 , 16). Find (a) P ( X < 6) (b) P ( X > 0) (c) P (2 ≤ X ≤ 3) (d) P ( X ≤ 1 . 53). 8 Let X ∼ N (10 , 25). Find x such that P ( X < x ) = 1 / 10. Give the answer to three signiﬁcant ﬁgures. 2...
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This note was uploaded on 03/12/2012 for the course MTH 4106 taught by Professor R.a.bailey during the Spring '12 term at Queen Mary, University of London.
 Spring '12
 R.A.Bailey
 Statistics

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