Quiz2-2007-2- test 2- 610 question 1

Sol ft t ft t c 4 let x p t t 1 p t

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Unformatted text preview: better chance of lasting for one more month (new or old)? Why? Show your work. 3 Sol) The ‘new’ one has better chance since = e− 1 P (T > 2) e−4 = = −1 = e−3 P (T > 1) e P (T > 1) P (T > 2|T > 1) (b) (4%) Find the probability density function for transformer life fT (t). Sol) FT (t) fT (t) (c) (4%) Let X = √ = P (T ≤ t) = 1 − P (T > t) = 1 − e−t = 2 2te−t , 2 t > 0. T . Find the probability density function for fX (x). Sol) Obviously, the range of X is [0, ∞). Consider 0 ≤ x < ∞. FX (x) = = P (X ≤ x) √ P ( T ≤ x) = P (T ≤ x2 ) = 1 − e−x =⇒ fX (x) = 4 4 4x3 e−x , x>0 8. A randomly chosen IQ test taker obtains a score that is approximately a normal random variable with mean 100 and standard deviation 15. What is the probability t...
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This document was uploaded on 11/01/2013.

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