Question: Let X be a r.v. with continuous d.f. FX, and define the r.v. Y as follows: Y = X If X ( C, and Y

Let X be a r.v. with continuous d.f. FX, and define the r.v. Y as follows: Y = X
If X ( C, and Y = C if X > C, where C is a constant. Then
(i) Determine the d.f. of the r.v. Y, FY.
(ii) Show that FY = F1 + F2, where F1 is a continuous d.f. and F2 is a step function?

Step by Step Solution

★★★★★

3.40 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

i In the first place PY C PX C 1 FX C Next F Y y PY y PY yX CPX C PY y X CP X C PX yX C ... 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)

742-M-S-P (6908).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a random variable that takes on nonnegative values and has distribution function F(x). Show that Hint: Integrate by parts. Illustrate this result by calculating E(X) by this method if X has...

Let X be a random vector that is split into three parts, X = (Y, Z, W). Suppose that X has a continuous joint distribution with p.d.f. f (y, z, w). Let g1(y, z|w) be the conditional p.d.f. of (Y, Z)...

Let X be a random variable for which the p.d.f f is as given in Exercise 3. Construct a random variable Y = r(X) for which the p.d.f. g is as given in Exercise 9. 1 -x 0 otherwise. for 0

Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment 1 utdallas.edu/~metin Outline Capacity Planning Product-to-plant Assignment utdallas.edu/~metin 2 Deterministic Capacity...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

Let X be a r.v. with d.f. F; i.e., F(x) = P(X ( x), x ( (. Then show that (i) P(X

Show that if a r.v. X has a continuous d.f. F(x), then the distribution of the r.v. Y = F(X) coincides with the distribution uniform on [0,1]. (The r.v. Y may not assume values 0 and 1, but for the...

Policy Choose two of the above design models, representations or evaluation methods, and explain how they would be done differently. Here is the related facts that might help to solve the problem -...

Hi please use the given information to answer each part of the problem and please include any drawing, or steps/formulas to improve my understanding of the problem if necessary. Thank you! Please...

Describe the AC-3 algorithm for enforcing arc consistency. If you need some support data, here it is: Support Details for the question - [5 marks] (e) Prove that the time complexity of the AC-73...

Remor Inc. has a constant debt-to-equity ratio policy. Company earnings are taxed. The unlevered value of the $5,000,000. Nevertheless, the company has debt in its capital structure. The levered wacc...

Calculating the Variable Overhead Spending and Efficiency Variances Refer to Cornerstone Exercise 9.6. Required: 1. Calculate the variable overhead spending variance using the formula approach. (If...

Question 3 ( 3 0 marks ) . The following option price quotations on Xerox stock are observed: Type of option Exercise Price ( E ) Option Premium ( V _ ( C ) or V _ ( P ) ) Xerox stock is currently...

Cost estimating should be performed: A. Before the work breakdown structure is created and before the budget is developed. B. Before the work breakdown structure is created and after the budget is...

This year Jan Rich, who is ranked number one in women's singles in tennis, and Marie Wacker, who is ranked number three, will play 4 times. If Marie can beat Jan 3 times, she will be ranked number...

Over the last two months, the Wilmington Phantoms have been encountering trouble with one of their star basketball players. During the last 30 games, he has fouled out 15 times. The owner of the...

Wisconsin Cheese Processor, Inc., produces equipment that processes cheese products. Ken Newgren is particularly concerned about a new cheese processor that has been producing defective cheese...

Gatewny Toum is choosing between twe bus models, one of which lasts longer than the other. Gateway's discount rate is 7%. It plans to continue with one of the two modely for the fo future. Based on...

Portfolio Risk and return assignment Fin 311. Fall 2022 Use the following table to answer questions 1 through 4. hosiment yuesunns, 1. Compute the expected rate of return for each of the three stocks...

If you carry an auto-liability-insurance requirement of 30/60/25 and are at fault for an accident that totals the other driver's car, will your insurance cover the replacement valuec at $26,700? What...