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Unformatted text preview: 3. [10 marks] Let X be a random variable distributed as ( ) 16 , 7 N . (a) Suppose ⎣ ⎦ X Y = (the integer part of X ). Calculate ( ) 8 = Y P . (b) Let . Find the r th moment of W . . [10 marks] lifetime characterizes the remaining survival time of a subject, given that the X e W = 4 The residual subject has already survived up to time t . Correspondingly, the mean residual lifetime is the remaining life expectancy conditional on survival at time t , which is defined as ( ) ( ) t T t T E t m > − =  for where T is the failure time. Show that the mean residual lifetime has an explicit onetoone ≥ t correspondence to the survival function ( ) ( ) ( ) ( ) ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − = ∫ t du u m t m m t S 1 exp ....
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This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.
 Fall '08
 SMSLee
 Statistics, Probability

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