Question: Let X be a random variable with quantile function F1. Assume the following three conditions: (i) F1(p) = c for all p in the interval

Let X be a random variable with quantile function F−1. Assume the following three conditions: (i) F−1(p) = c for all p in the interval (p0, p1), (ii) either p0 = 0 or F−1(p0) < c, and (iii) either p1 = 1 or F−1(p) > c for p > p1. Prove that Pr(X = c) = p1 − p0.

Step by Step Solution

★★★★★

3.48 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We know that PrX c Fc Fc We will prove that p1 F c and p 0 Fc For each p 0 1 d... View full answer

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)

602-M-S-C-R-V (1330).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a random variable with mean and variance 2, and let X1, X2,., Xn be a random sample of a continuous random variable with cumulative distribution function F(x). Find E[F(X(n))] and E[F(X(1))].

Let X be a random variable with E(X) = μ and V (X) = σ2. Show that the function f(x) defined by

Let X be a random variable with range [1, 1] and let fX (x) be the density function of X. Find (X) and 2(X) if, for |x|

Consider the Markov Chain, Xn, on the states i = 0, 1, 2, . . . with transition matrix given by pi,i1 = p i = 1, 2, . . . pi,i+1 = 1 p i = 0, 1, . . . p0,0 = p where 0

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

lup ] (d) Show how a generating (or "mother") wavelet (x) can spawn a family of "daughter" wavelets jk(x) by simple shifting and scaling operations, and explain the advantages of representing...

10/29/2015 Week 6 Assignment YINWEI LIU CED 6030, section 02, Fall 2015 Instructor: He Wang WebAssign Week 6 Assignment (Homework) Current Score : - / 114 Due : Wednesday, November 4 2015 11:59 PM...

For each statement below, say whether it's true or false; if true without further assumptions, briefly explain why it's true (and ? extra credit ? what its implications are for statistical...

The best definition for nonparametric statistics I can think of is when data does not fit inside the normal parameters of a normal distribution, it calls for the use of this statistical method....

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

According to the Solow model an increase in the growth rate of the labor force will: O A. increase income per worker O B. decrease income per worker O C. have no change on income per worker O D. not...

Explain why it is somewhat misleading to assert that the corporate form provides limited liability for its owners, whereas the partnership form saddles its owners with unlimited liability.

Why would a company want to provide its customers with only a 95% demand service level rather than a 100% level?

Why have so many firms rushed to implement ERP systems over the past twenty years?

Recall the data set of soil compressibility measurements given in DS 6.6.6. Construct a 9995 one-sided confidence interval that provides an upper bound on the average soil compressibility. Can the...

Shows the data obtained from a paired experiment performed to examine which of two assembly methods is quicker on average. A random sample of 35 workers on an assembly line were selected and all were...

Researchers into the genetic disease sickle cell anemia are interested in how red blood cells adhere to endothelial cells, which form the innermost lining of blood vessels. A set of 14 blood samples...

11. Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolios expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent. Amanda...

A stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 43.37 - 2 48.35 $ .60 3 57.27 .63 4 45.35 .80 5 52.27 .85 6 61.35 .93 What are the arithmetic and geometric...

The following data for the Height and Weight variables are provided to construct a scatterplot: Therefore, based on the information provided above, the following scatter plot is obtained by simply...