Question
Asked Feb 22, 2019
27 views

Recall that we say that a random variable X is in the vector space L^2 if it has finite second moment, EX^2 In this problem we will understand a bit better the geometry of the vector space L^2
(1) Show that ||X||_2 = √EX^2 is a norm

check_circle

Expert Answer

Step 1

Properties of a norm:

In order to prove that ||X||2 = √E(X2) is a norm, it must satisfy 3 conditions:

  • Positivity,
  • Homogeneity,
  • Sub-additivity.
Step 2

Proof of positivity:

To prove: ||x||2 ≥ 0 for all x ϵ X and x = 0 if and only if x = 0.

Proof:

fullscreen
Step 3

Proof of homogeneity:

To prove: For all x ϵ X, ||cx||2 = |c|.||x||2 for all real c...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Probability

Other

Related Probability Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: The table shows the​ distribution, by age and​ gender, of 30.1 million people who live alone in a ce...

A: Conditional probability of two events:The conditional probability is the probability of one event gi...

question_answer

Q: The probability density function for a continuous random variable X is given by               f(x) =...

A: In this question we have the pdf and using which we have to find the 70th percentile.

question_answer

Q: Among a student group 49% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the...

A: Probability of students using Google chrome= 0.49Probability of students using other browsers = 0.51

question_answer

Q: Suppose we want to choose 2 colors without replacement, from the 4 colors red,blue,green, and purple...

A: a.Find the number of ways in which 2 colours can be chosen among the 4 colours without giving import...

question_answer

Q: Use a truth table to determine whether this argument is valid or invalid: VALID INVALID p V q TITIT ...

A: The given arguments:The given symbolic form arguments and the argument (not yet verified whether cor...

question_answer

Q: 8 points) Identify the critical t. An independent reedom and the crtical random sample is selected f...

A: Given:Sample Size \'n\'Confidence LevelDegree Of FreedomCritical Value t*1290  2795  1198  1799  

question_answer

Q: This is for a Linear Algebra class. Please provide explanations for the answer (3) In the casino gam...

A:  Part(a)We have been given that in a casino game of roulette, a ball is spun around a wheel with 38 ...

question_answer

Q: A local university has 2,815 Hispanic students out of a total of 20,250 students. How many more Hisp...

A: Assumption: The Hispanic population ratio in the country is 17% (approximately).The university has 2...

question_answer

Q: in cribbage the card game, I hand of six cards is dealt from a normal deck of 52 cards. What is the ...

A: Gven that a hand of six cards is dealt from deck of 52 cards.We need probability that we have all fi...