Question: 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

Let X be a random variable that takes on nonnegative values and has function F(x). Show that

E(X) = P(X j+ 1). j=0

Hint: Integrate by parts.
Illustrate this result by calculating E(X) by this method if X has an exponential F(x) = 1 − e−λx for x ≥ 0, and F(x) = 0 otherwise.

E(X) = P(X j+ 1). j=0

Step by Step Solution

★★★★★

3.39 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Integrating by parts we have EX xdF 2 z1 Fx 1 F2x 1F 1 Fxdx To justify this argment we have to sho... 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)

M-S-C-R-V (167).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a random variable that takes on values between 0 and c. That is, P{0 X c} = 1. Show that Var(X) c2/4 One approach is to first argue that E[X2] cE[X] and then use this inequality to show...

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. Assume that for people under 50 years old, x has a distribution...

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean Î¼ = 7500...

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...

GIVE DETAILED WORKING IN ALL QUESTIONS. Suppose that a game is to be played with a single die assumed fair. In this game a player wins $20 if a 2 turns up, $40 if a 4 turns up; loses $30 if a 6 turns...

Let X be a random variable that takes only non-negative integer values. Then show that E(X) = +X i=1 P (X i)Let X and Y be 2 independent r.v.'s that each follow a Geometric law of parameter p. 1....

Let X be a random variable with the density f(x)={x(1+)0x>1x1 where >0 is a real parameter. (a) Show that the Value-at-Risk of X at level (where X is to be treated as the loss variable) is given by...

4) (10) Let X be a random variable, which takes values 0,1,2,3. The distribution table for X is given below. X Probability function 0 2k 3k/2 2 3k/2 3 2k a) Find the value of k. Show your work. b)...

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...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

1.The direct write-off method of accounting for the impairment of receivables a.is never acceptable. b.is specifically disallowed under IFRS. c.is an acceptable method when the effect of not applying...

"In the compound republic of America, the power surrounded by the people his first divided between two distinct government, and then the portion allotted to each is so divided among distinct and...

17. LO.1, 2, 4, 11 Simon owns stock that has declined in value since acquired. He has decided either to give the stock to his nephew, Fred, or to sell it and give Fred the proceeds. If Fred receives...

Consider the probability distribution shown here: a. Calculate Î¼, Ï2, and Ï. b. Graph p(x). Locate Î¼, Î¼ 2Ï, and Î¼ + 2Ï on...

During the current year, merchandise is sold for $275,000 cash and $990,000 on account. The cost of the merchandise sold is $950,000. What is the amount of the gross profit?

Journalize the following merchandise transactions: a. Sold merchandise on account, $60,000 with terms 1/10, n/30. The cost of the merchandise sold was $40,000. b. Received payment less the discount.

During the current year, merchandise is sold for $775,000. The cost of the merchandise sold is $426,250. a. What is the amount of the gross profile? b. Compute the gross profile percentage (gross...

For the year ended February 28, 2009, Best Buy reported revenue of $45,015 million. Its gross profit was $10,998 million. What was the amount of Best Buys cost of merchandise sold?

What is the basic advantage of using interrupt-initiated data transfer over transfer under program control without an interrupt?

Ted McKay has just bought the common stock of Cullumber Corp. Management of Cullumber expects the company expects to grow at the following rates for the next three years: 35 percent, 30 percent, and...

Finding a present value is the reverse of finding a future value. Which of the following is true about finding the present value of cash flows? O Finding the present value of cash flows tells you how...

In this assignment, you will use this information to create an income statement and then analyze it for profitability. Selected accounts for Jackson, Inc. are listed below along with their balances...