This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: λx ) ´³ 1 λx exp(λx )exp(λx ) λ ´ 2. Consider the uniform distribution F ( x ) = x/ω on [0 ,ω ]. for some arbitrary ω . (a) Compute the probability density function. f ( x ) = F ( x ) = 1 ω (b) Compute its expectation. E [ X ] = Z ω xf ( x ) dx = Z ω x ω dx = ± x 2 2 ω ² ω x =0 = ω 2 (c) Compute the expectation of γ ( x ) = x 2 . E [ γ ( X )] = Z ω x 2 f ( x ) dx = Z ω x 2 ω dx = ± x 3 3 ω ² ω x =0 = ω 2 3 (d) Compute its hazard ratio. λ ( x ) ≡ f ( x ) 1F ( x ) = 1 ω 1x ω = 1 ωx (e) Compute the conditional expectation E [ X  X < x ]. 2 E [ X  X < x ] = 1 F ( x ) Z x tf ( t ) dt = ω x Z x t 1 ω dt = 1 x ± t 2 2 ω ² x t =0 = ³ 1 x ´³ x 2 2 ω ´ = x 2 3...
View
Full
Document
This note was uploaded on 09/06/2009 for the course MATH 103 taught by Professor Anh during the Spring '09 term at University of California, Berkeley.
 Spring '09
 Anh
 Math, Probability

Click to edit the document details