Question: Show that if X is a random variable with the mean for which f(x) = 0 for x < 0, then for any positive

Show that if X is a random variable with the mean µ for which f(x) = 0 for x < 0, then for any positive constant a, P(X ≥ a) ≤ µ/a This inequality is called Markov’s inequality, and we have given it here mainly because it leads to a relatively simple alternative proof of Chebyshev’s theorem.

Step by Step Solution

★★★★★

3.35 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Px a QE... 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)

583-S-J-P-D (723).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Show that if X is a random variable with mean and variance 2, and if X* = (X )/ is the standardized version of X, then

Consider the Cauchy family defined in Section 3.3. This family can be extended to a location-scale family yielding pdfs of the form The mean and variance do not exist for the Cauchy distribution. So...

Show that if X is a random variable having the Poisson distribution with the parameter and , then the moment-generating function of Z = X / That is, that of a standardized Poisson random...

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...

kindly solve showing your steps 1. (a) Consider an individual making choices over two goods, x and y with initial prices Px = 20 and py = 10, with income I = 1000. If the individual has the utility...

5 Just One Tail, Please 5 Just One Tail, Please Let X be some random variable with nite mean and variance which is not necessarily non- negative. The extended version of Markov's Inequality states...

Modeling the Height of the U.S. Population II 1 point possible {graded} Continuing from the problem above, your goal is to answer the question of interest "Were people in the U.S. taller in 2018 than...

Kindly help me solve this problem A firm uses inputs of labor, L, and capital, K, to produce its output, Q, according to the production function Q=f(X,L)-9LUSKVS. The firm is a price-taker in the...

1 Just One Tail, Please Let X be some random variable with nite mean and variance which is not necessarily non- negative. The extended version of Markov's Inequality states that for a non-negative,...

statistics , calculus and probability questions - need help Question 12 3 pts Suppose that X is a random variable with a mean of 6 and variance of 8; Y is a random variable with a mean of -10 and...

Identify the dominant religion in each of the following countries: (a) Brazil, (b) China, (c) India, (d) Ireland, (e) Mexico, (f) Russia, and (g) Thailand.

_., let the universe be the set Z+. Let X = (1, 2, 3, 4, 5) and let Y be the set of positive, even integers. In set- builder notation, Y = (2n |ne Z+). 7, give a mathematical notation for the set by...

8 . A company calculated the predetermined overhead based on an estimated overhead of $ 7 0 , 0 0 0 , and the activity for the cost driver was estimated as 2 , 5 0 0 hours. If product A utilized 1 ,...

Which of the following statements best captures how those that support sustainable development look at the future for the global environment? a) Ecological collapse is inevitable. b) Fossil fuels...

At four community health centers on Cape Cod, Massachusetts, 15,164 patients were asked to respond to questions designed to detect depression (The Boston Globe, June 11, 2008). The survey produced...

Let P (A) = 0.65, P(B) = 0.30, and P(A | B) = 0.45. a. Calculate P (A B). b. Calculate P (A B). c. Calculate P (B | A).

Let P (A) = 0.55, P (B) = 0.30, and P (A B) = 0.10. a. Calculate P (A | B). b. Calculate P (A B). c. Calculate P ((A B)c).

Indicate whether each of the following would be in the section of financial statements identified as a) current asset b) property, plant, and equipment c) current liability d)revenue or e) expense 1....

What is the realized return percent? The following table contains prices and dividends for a stock. All prices are after the dividend has been paid. If you bought the stock on January 1 and sold it...

A terminated employee is not entitled to COBRA benefits if he is terminated for gross misconduct. Group of answer choices True False