Question: Let X be a random variable with E[X] 1. Show that E X2 1 if X is not degenerate. Hint: Use Jensens

Let X be a random variable with E[X] Æ 1. Show that E

£

X2¤

È 1 if X is not degenerate.

Hint: Use Jensen’s inequality.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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

Students Have Also Explored These Related Applied Statistics And Probability For Engineers Questions!

Q:

Please solve (i) and (ii)(b) only Al. (i) Let X be a random variable with E[|X]] 0. Prove the Chebyshev inequality: for any & > 0, P ( IX | ZE )S E[IX | ~ ] Ea [5 marks] (ii) Let Xn, n 2 1, be a...

Q:

Problems 1. Probability Refresher. Let X be a random variable which is 1 with probability 1/100 and 0 with probability 99/100. (a) (2 points) What is the expected value E[X]? (b) Suppose you draw n...

Q:

1. A portfolio manager is expected to stay within 75 basis points of a benchmark index 90 percent of the time. The manager meets this objecti ve in six out of eight quarters. Calculate the...

Q:

Consider the Markov Chain, Xn, on the states i = 0, 1, 2, . . . with transition matrix given by pi,i1 = p i = 1, 2, . . . pi,i+1 = 1 p i = 0, 1, . . . p0,0 = p where 0

Q:

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...

Q:

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

Q:

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...

Q:

Consider the following situation. Suppose we have two fair dice, D1 with 5 red sides and 1 white side and D2 with 1 red side and 5 white sides. We pick one of the dice randomly, and throw it...

Q:

2 4. (Paley-Zygmund's inequality) (a) Let X be a random variable such that EX > 0 and EX? t) or otherwise, show that P(X > t) > - (E(X ) -t)2 EX2 OKt 0 and variance o' satisfying 0 H - 0 ) 2 2 + 12...

Q:

Help me solve this exercise. DIS. 7. Cantelli's inequality. Let X be a random variable with finite variance, o2. (a) Prove that, for 1>0, 02 P(X - EX > 3) ) 22 +02 (b) Find X assuming two values...

Q:

Pete's Plastics manufactures plastic at plants in Miami, St. Louis and Cleveland. Pete needs to ship plastic to customers in Pittsburgh, Atlanta and Chicago. He wants to minimize the cost of shipping...

Q:

Question 1 Define and explain the following terms. Please use diagrams and relevant examples where possible (3 marks each) a) Price Floor b) Producer Surplus e) Depreciation d) Law of Demand e)...

Q:

Going public establishes a true market value for the firm and ensures that a liquid market will always exist for the firm's shares. Question 8 options: TrueFalse

Q:

The total cost to produce x large jewelry-making kits and y small ones is given by C(x, y) = 2x 2 + 6y 2 + 4xy + 10. If a total of ten kits must be made, how should production be allocated so that...

Q:

Show that the set of \(2 n \times 2 n\) real matrices of the form \[ \left(\begin{array}{rr} A & B \\ -B & A \end{array}ight) \] is closed under matrix addition and multiplication. Show also that the...

Q:

Find the survival distribution \(P\) associated with the hazard measure \[ \theta(d t)=\left\{\begin{array}{cc} d t /(1-t) & 0

Q:

In Exercise 14.10, the null hypothesis of no treatment effect \(H_{0}: \tau=0\) is the left endpoint of the parameter interval \(\tau \in[0,2 \pi)\). Explain why this is not a boundary point in the...

Q:

using LabVIEW 2. Create a coin toss program that generates that simulates the toss of a coin. Use the "Select" function in the Comparison palette, where string constants "Heads" is wired to the True...

Q:

Which of the following is not a type of operating system? A ) Real - time B ) Network C ) Distributed D ) Sequential

Q:

List cities _ list is created with two cities read from input. Then, list state _ codes _ list is created with two state codes read from input. On one line, output: state _ codes _ list's first...