## Question

###### 12. Let the d.f. have density that - continuous and positive on am interval such that F(b) _ F(a) < 0. (The results are fact valid if we only suppose that F is continuous. )(a) Show that if X has density then Y = F(T) is uniformly distributed on (0. 1). (b) Show that if U u(O. 1) . then F-!(U) has density

12. Let the d.f. have density that - continuous and positive on am interval such that F(b) _ F(a) < 0. (The results are fact valid if we only suppose that F is continuous. ) (a) Show that if X has density then Y = F(T) is uniformly distributed on (0. 1). (b) Show that if U u(O. 1) . then F-!(U) has density

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