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Unformatted text preview: if β 1 ( t ) = kβ ( t ), then 1F 1 ( x ) = [1F ( x )] k . 1 10. Optional Problem ( Solution Will be provided, but you need not submit it ) The space of an experiment consists of all points in the unit interval (0 , 1). All intervals are events with probability equal to their length: P [0 ≤ ζ ≤ y ] (1) We are given a continuous, monotone increasing function y = G ( x ), such that G (∞ ) = 0, G ( ∞ ) = 1. With x = H ( y ) its inverse, we have G [ H ( y )] = y for any y in the interval (0,1). A r.v. x is so deFned that x ( ζ ) = H ( ζ ), where ζ is an outcome of the preceding experiment. Show that the distribution of x equals G ( x ). 2...
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 Spring '05
 Roychowdhary
 Probability theory, Order theory, Equals sign, Monotonic function, Vwani Roychowdhury

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