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Unformatted text preview: ± λ λ + x ² α . [6] S T ( x ) = 1F T ( x ) = 1Z x f T ( s ) ds = 1Z x αλ α ( λ + s ) α +1 ds = λ α ( λ + x ) α 5 (b) Derive an expression for μ x . [5] μ x = f T ( x ) S T ( x ) = α λ + x Note that f T ( x ) and S T ( x ) are given in the question. 6 (c) Derive an expression for S T x ( t ). [5] S T x ( t ) = S T ( x + t ) S T ( x ) = ± λ λ + x + t ² α ± λ λ + x ² α = ³ λ + x λ + x + t ´ α . 7 (d) Using (b) and (c), or otherwise, ﬁnd an expression for f T x ( t ). [5] f T x ( t ) = S T x ( t ) μ x + t = ± λ + x λ + x + t ² α α λ + x + t . 8...
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This note was uploaded on 03/20/2011 for the course ACTSC 232 taught by Professor Matthewtill during the Summer '08 term at Waterloo.
 Summer '08
 MATTHEWTILL

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