For every random variable X, show that |E(X)| E(|X|).

Question:

For every random variable X, show that |E(X)| ≤ E(|X|).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

See More Books

Question Posted: Nov 25, 2015 04:04 AM

See More Questions

Let f(x) = 1/[(1 + x2)], < x < , be the pdf of the Cauchy random variable X. Show that E(X) does not exist.
For any random variable X for which EX2 and E|X| exist, show that P(|X| > 6) does not exceed either EX2/b2 or E|X|/6, where b is a positive constant. If f(x) = e~x for x > 0, show that one bound is...
Show that (a) Show that E(X - ) = 0, 2 = E(X 2 ) - 2 . (b) Prove (10)-(12). (c) Find all the moments of the uniform distribution on an interval x b. (d) The skewness of a random variable X is...
A- Farah Corporation has provided the following production and total cost data for two levels of monthly production volume. The company produces a single product which it sells at $132.7 per unit...
Byrd Company is a manufacturer of appliances for both residential and commercial use. The companys accounting and financial reporting system is primarily designed to meet external reporting...
If you are planning an acquisition that is motivated by trying to acquire expertise, you are basically seeking to gain intellectual capital. What concerns would you have in structuring the deal and...
Consider a fictitious dataset of $n=100$ observations with $s_{y}=80$. We run a regression with three explanatory variables to get $s=50$. a. Calculate the adjusted coefficient of...
Circular copper rod of diameter D = 1 mm and length L = 25 mm are used to enhance heat transfer from a surface that is maintained at Ts.1 = 100C. One end of the rod is attached to this surface (at x...
As an engineering challenge, a group of high schoolers are trying to create an apparatus to safely catch a dropped egg. A USDA-rated large chicken egg with a mass of 57 grams is to be dropped from...
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive...
Suppose that a random sample of n observations is taken from a Poisson distribution for which the value of the mean is unknown ( > 0), and the value of = e must be estimated by using the squared...
Suppose that a random sample X1, . . . , Xn is to be taken from the uniform distribution on the interval [0, ] and that is unknown. How large a random sample must be taken in order that Pr(| max{X1,...
How can data integrity be ensured when conducting e-business? Why is it critical to e-business?
An increasingly popular device for improving air flow through nasal passages is the nasal strip, which consists of two flat, polyester springs enclosed by an adhesive tape covering. Measurements show...
3) A mass of 100 kg is hung from a spring in a local gravitational field where g = 9.806 m/s, and the spring is found to deflect 25 mm. if the same mass is taken to a planet where g = 5.412 m/s, how...
A car accelerates at -1.80 m/s for 3.81 s. The car travels 26.5 m in that time. What is the final velocity of the car? Vf = [ ? ] m/s
Two coils are placed close together in a physics lab to demonstrate Faraday's law of induction. A current of 9.00 A in one is switched off in 1.20 ms, inducing a 2.00 V emf in the other. What is...
An atom in a solid vibrates at 1 1 . 6 THz with amplitude 1 0 pm . Find the a ) atom's maximum speed and b ) maximum acceleration. If it is a carbon atom, c ) what's its energy?
In Exercises 1535, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 5 = 5(x + 3) + 2x -
Inexhaustible collections of ONPOs are not required to be capitalized or depreciated, if certain criteria are met. Why is this so, and what accounting and reporting recognition, if any, is required...
What diagnostic plot can you use to determine whether the assumption of equal variance has been violated? What should the plot look like when the variances are equal for all values of x?
How is the cost of a plane flight related to the length of the trip? The table shows the average round-trip coach airfare paid by customers of American Airlines on each of 18 heavily traveled U.S....
An experiment was designed to compare several different types of air pollution monitors. The monitor was set up, and then exposed to different concentrations of ozone, ranging between 15 and 230...
Determine the exact solution of the system given below using addition or subtraction of matrices or scalar multiplication 5x - ey + 3x+2y- z = -2 . = 1 0 4x-7y+ 5z =
We need to be able to describe systems to assist with development, to assist with use, and to assist with maintenance. To that end, diagrams provide a concise, semi-formal way of describing a system....
Determine when the parametric curve x = 31261+2 and y = 4t - is concave up.

For every random variable X, show that |E(X)| E(|X|).

Question:

Step by Step Answer:

Suppose that X has a continuous distribution for which the pdf is f Then Suppose first t...View the full answer

Probability And Statistics

Students also viewed these Statistics questions