Question: Let X have the uniform distribution on the interval [a, b], and let c > 0. Prove that cX + d has the uniform distribution

Let X have the uniform distribution on the interval [a, b], and let c > 0. Prove that cX + d has the uniform distribution on the interval [ca + d, cb + d].

Step by Step Solution

★★★★★

3.40 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let Y cX d The inverse transformation is x y dc Assume that c 0 The derivative of the i... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

602-M-S-C-R-V (1395).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Let F be an arbitrary c.d.f. (not necessarily discrete, not necessarily continuous, not necessarily either). Let F1 be the quantile function from Definition 3.3.2. Let X have the uniform distribution...

Q:

Let X have the uniform distribution on the interval [0, ], and suppose that we wish to test the hypotheses H0: 1, H1: >1. We shall consider test procedures of the form reject H0 if X c. For each...

Q:

Let F1 be defined as in Eq. (12.3.7). Let U have the uniform distribution on the interval [0, 1]. Prove that F1(U) has the c.d.f. in Eq. (12.3.6).

Q:

Let X have a uniform distribution on the interval (0, 1). Given X = x, let Y have a uniform distribution on (0, x). (a)TheconditionalpdfofY,giventhatX=x,isfY|X(y|x)=1 for0 x since Y|X ? U(0,X). Show...

Q:

Let X have a uniform distribution on the interval (0,1). Given that X = x, let Y have a uniform distribution on the interval (0, x + 1). (a) Find the joint pdf of X and Y. Sketch the region where...

Q:

Please help me to do Q3 and Q4 with steps. Q3 (12 marks) Let X has a uniform distribution on the interval (0,1). Give that X=x, Yhas a uniform distribution on the interval (0,x). Find the marginal...

Q:

Ans with full steps please Q3 (12 marks) Let X has a uniform distribution on the interval (1,2). Give that X=x, Y has a uniform distribution on the interval (0,x). Find the marginal p.d.f. of Y. Q4....

Q:

kindly solve the question step by step and solve all the parts. I have give all the information.kindly solve question as soon as possible. 2. Let fX,Y(x,y)={Cexp(21(x2+y2))0if0xyotherwise (a) Compute...

Q:

5. A strand of string of length L > 0 is cut into two pieces of lengths X and L - X. X follows a uniform distribution over the interval (0, L). Let Y be the length of the longer piece of string. (a)...

Q:

5. A strand of string of length L > 0 is cut into two pieces of lengths X and L - X. X follows a uniform distribution over the interval (0, L). Let Y be the length of the longer piece of string. (a)...

Q:

According to the U.S. Census Bureau publication Demographic Profiles, a relative-frequency distribution of the U.S. resident population by region in 2000 was as follows. A simple random sample of...

Q:

A cognitive psychologist wishes to determine how short-term verbal memory capacity varies under three distraction conditions: no distraction, music, and music plus video. Thirty college students are...

Q:

The following statement permits assembly if arg 1 is exactly the same as arg 2 ? ( casesensitive comparison ) : IFIDN

Q:

Why is early supplier involvement a good way to integrate the supply chain?

Q:

A simple linear regression model is to be fitted to the data set of temperature and yield values for bacteria cultivation in DS 12.11.8. with temperature as the explanatory variable and yield as the...

Q:

A data set has n = 20. 20i=1 xi = 8.552, 20i=1yi, = 398.2, 20i=1 x2i, = 5.196. 20i =1 y2i = 9356 and 20i=1 = 216.6. Calculate ^0, ^1, and ^2. What is the fitted value when x = 0.5?

Q:

A data set has n = 30,30i=1, x i = -67.11. 30i=1 1322.7, 30i=1 x2l = 582.0, 30i=1 y2i = 60,600 and 30i=1 xiy1 = -3840. Calculate ^0 ^1 and ^2. What is the fitted value when x = -2.0?

Q:

need to ROCE for 14 and 17 X CONSE x + tombetoon.com/debedamer- fackboard cond252F apter Exercices 0 Help Check my Exercise 6-11 Calculating ROCE for Kroger (LO6-4) This exces but around Kuger's...

Q:

Common stock value Variable growth Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just completed, Grips earned $3.66 per share and paid cash dividends...

Q:

Using the lme4 package, we can call this data set with the command: data(Arabidopsis) Access "Package 'lme4,'" to retrieve data on genetic variation in responses to fertilization and simulated...