This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: if β 1 ( t ) = kβ ( t ), then 1-F 1 ( x ) = [1-F ( 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...
View Full Document
- Spring '05
- Probability theory, Order theory, Equals sign, Monotonic function, Vwani Roychowdhury