Question

Let x be a continuous random variable, let alpha in R such that P(x>=alpha )>0, and define F:R->[0,1] by F(z)=P(x<=z|x>=alpha ) Show that, F(z)={((F_(x)(z)-F_(x)(alpha ))/(1-F_(x)(alpha )) if z>=alpha ),(0 if z<alpha .):} where F_(x) is the cumulative distribution function of x. Note: it is possible to show that F is the distribution function of a random variable Z. For example, if x models the lifespan of a phone, then Z is the remaining lifespan if we assume the phone is operational up to time alpha .

Name: let x be a continuous random variable let alpha in r such that pxalpha 0 and define fr 01 by fzpxzxalpha show that fzfxz fxalpha 1 fxalpha if zalpha 0 if zalpha where fx is the cumulativ 91357
Uploaded: 2023-04-30T05:11:45-08:00
Duration: 3 min 59 s
Channel: Madhur L
Description: let x be a continuous random variable let alpha in r such that pxalpha 0 and define fr 01 by fzpxzxalpha show that fzfxz fxalpha 1 fxalpha if zalpha 0 if zalpha where fx is the cumulativ 91357

          Let x be a continuous random variable, let alpha  in R such that P(x>=alpha )>0, and define
F:R->[0,1] by
F(z)=P(x<=z|x>=alpha )
Show that,
F(z)={((F_(x)(z)-F_(x)(alpha ))/(1-F_(x)(alpha )) if z>=alpha ),(0 if z<alpha .):}
where F_(x) is the cumulative distribution function of x.
Note: it is possible to show that F is the distribution function of a random variable Z. For example, if x models the lifespan of a phone, then Z is the remaining lifespan if we assume the phone is operational up to time alpha .

Added by William G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/30/2023

Step 1

We are given a continuous random variable x and a real number α such that P(x >= α) > 0. We define a function F: R -> [0,1] where F(z) = P(x <= z | x >= α). Here, F_(x) represents the cumulative distribution function (CDF) of x. Show more…

Show all steps

Thanks for your feedback!

Let x be a continuous random variable, let alpha in R such that P(x>=alpha )>0, and define F:R->[0,1] by F(z)=P(x<=z|x>=alpha ) Show that, F(z)={((F_(x)(z)-F_(x)(alpha ))/(1-F_(x)(alpha )) if z>=alpha ),(0 if z<alpha .):} where F_(x) is the cumulative distribution function of x. Note: it is possible to show that F is the distribution function of a random variable Z. For example, if x models the lifespan of a phone, then Z is the remaining lifespan if we assume the phone is operational up to time alpha .