Question: Suppose that X is a random variable with mean and variance 2, and that the fourth moment of X is finite. Show that E[(X

Suppose that X is a random variable with mean μ and variance σ2, and that the fourth moment of X is finite. Show that
E[(X − μ)4] ≥ σ4.

Step by Step Solution

★★★★★

3.37 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Let Y X 2 The... View full answer

blur-text-image
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)

Word file Icon

602-M-S-C-R-V (1469).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Suppose that X is a random variable having a continuous distribution with p.d.f. f (x) and c.d.f. F(x), and for which Pr(X > 0) = 1. Let the failure rate h(x) be as defined in Exercise 18 of Sec....

Q:

Suppose that X is a random variable such that E(Xk) = 1/3 for k = 1, 2, . . . . Assuming that there cannot be more than one distribution with this same sequence of moments (see Exercise 14),...

Q:

Suppose that X is a negative binomial random variable with p _ 0.2 and r _ 4. Determine the following: (a) E(X1) (b) P(X =20) (c) P(X =19) (d) P(X =21) (e) The most likely value for X

Q:

Let X be a random variable with mean and variance 2 such that the fourth moment E[(X ) 4 ] exists. The value of the ratio E[(X ) 4 ]/ 4 is often used as a measure of kurtosis. Graph each of the...

Q:

Let X be a random variable with mean and variance 2 such that the third moment E[(X ) 3 ] about the vertical line through exists. The value of the ratio E[(X ) 3 ]/ 3 is often used as a measure...

Q:

A randomized algorithm is said to give an (,)-approximation for the value of V if the output X of the algorithm satises P(|X V| ) . (Chebyshev Inequality) If X is a random variable with mean and...

Q:

If X be a random variable with mean and variance 2 and suppose that h(x) is differentiable function with h'() 6 not equal to 0, then the expectation and variance of Y = h(X) can be approximated as...

Q:

In Chapter 9, the concept of parameter estimation will be discussed at length. Suppose X is a random variable with mean and variance 2 = 1.0. Suppose also that a random sample of size n is to be...

Q:

8.73 In Chapter 9, the concept of parameter estimation will be discussed at length. Suppose X is a random variable with mean and variance 2 = 1.0. Suppose also that a random sample of size n is to...

Q:

Let X be a random variable with mean and variance 2 . Given two independent random samples of sizes n1 and n2, with sample means X 1 and X 2. Let X = aX 1+(1a)X 2, 0

Q:

What are the three motives for holding money according to Keynes's theory of money demand? Explain each motive.

Q:

Let X have p.d.f. Prove that the m.g.f. (t) is finite for all t 0 but for no t > 0. if x > 1, x 0 otherwise. f(x) =

Q:

Which of the following is not an example of misappropriation of assets? Group of answer choices The president of the company utilizes the organization's cash to add a floor to her 1 5 , 0 0 0 square...

Q:

When analyzing the supply chain management foundation element supply, what are some of the specific issues Cyber Logic Systems must address?

Q:

Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two people shaking hands, or a nurse squeezing a patient's forearm to stop bleeding. The...

Q:

Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter. a. Determine the value of the fourth spread. b. Are there any outliers in the sample? Any extreme...

Q:

The following data on distilled alcohol content (%) for a sample of 35 port wines was extracted from the article "A Method for the Estimation of Alcohol in Fortified Wines Using Hydrometer...

Q:

What is data sorting? Why is data sorting so important?

Q:

"This is everything that is provided and must be possible to resolve!" An American car manufacturer called Agnelli Inc. produces and sells variants of the Nuova 500 all over the world. In addition to...

Q:

On 4th October 2022, an open-ended managed fund had 8,420 units on issue, and held the portfolio described in the table below. The price for each share is the market price that day at 4:00pm. Share...