Practice Questions 3 Answer

Practice Questions 3 Answer - -q . ii. E ( N ) = q (1-q )...

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Answers to Practice Questions 3 – ACTSC 431/831, FALL 2011 1. (a) Pr { X < 1 } = 0 . 75. (b) The distribution of X is neither DFR nor IFR. (c) X 4 has a heavier tail than X . 2. (a) We have a = 600. Then, V ar ( X ) = 35 . 42. (b) We have F X ( x ) = Z x -∞ f X ( t ) dt = 0 , x < 0 , 0 . 06 x, 0 x < 5 , 0 . 1 x - 0 . 2 , 5 x < 10 , 1 - 200 x 3 , x 10 . (c) The probability is Pr { 4 < X < 8 } = 0 . 36. 3. (a) V ar ( N 1 ) = 39 . 67 . (b) Pr { N 1 < 5 or N 2 < 5 } = 0 . 00057 . 4. Pr { N 3 } = 0 . 9988. 5. (a) i. It is easy to check that the distribution of N is in the ( a,b, 1) class with a = q and b =
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Unformatted text preview: -q . ii. E ( N ) = q (1-q ) ln(1-q ) and V ar ( N ) =-q (1-q ) 2 ln(1-q ) 1 + q ln(1-q ) . (b) i. E ( N ) = ( a + b )(1-p )+ p 1 1-a . ii. V ar ( N ) = (1+( a + b ) p-p 1 ) [ ( a + b )(1-p )+ p 1 ] (1-a ) 2 . 6. (a) E ( S ) = 3 and V ar ( S ) = 3 . (b) S has a Poisson distribution with mean 3. (c) The probability is Pr { S 4 } = 0 . 35273 . 1...
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