Calculate E(x^2) Given I.I.D. N(0,1) Random Variables

  • Thread starter Thread starter James1990
  • Start date Start date
  • Tags Tags
    Expectation
Click For Summary
To calculate E(x^2) for i.i.d. random variables distributed as N(0,1), one can use the relationship between variance and moments. The variance of a standard normal distribution is 1, and the mean is 0. Applying the formula Var(X) = E[X^2] - {E[X]}^2, we find that E[X] = 0 simplifies the equation to E[X^2] = Var(X). Therefore, E(x^2) equals 1 for standard normal random variables. Understanding these properties is essential for accurate calculations.
James1990
Messages
2
Reaction score
0
How to calculate E(x^2) given that x are i.i.d random variables distributed as a standard normal i.e. N(0,1) ?
Thank you.
 
Physics news on Phys.org
James1990 said:
How to calculate E(x^2) given that x are i.i.d random variables distributed as a standard normal i.e. N(0,1) ?
Thank you.

Hey James1990 and welcome to the forums.

Do you know the relationship for Variance to second and first order moments?

[HINT: Var(X) = E[X^2] - {E[X]}^2].

What do you know about the mean and variance of your distribution?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
View full post »

Similar threads

Undergrad Sampling theory and random sample
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad On the expected value of a sum of a random number of r.v.s.
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Mutual information of a noisy function
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Maximum likelihood to fit a parameter of this model
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Statistical modeling and relationship between random variables
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Computing the expectation of the minimum difference between the 0th i.i.d.r.v. and ith i.i.d.r.v.s where 1 ≤ i ≤ n
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Understanding extinction probability in simple GWP
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad The characteristic function of order statistics
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Help understanding conditional expectation identity
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is this conditional expectation identity true?
  • · Replies 1 ·
Replies
1
Views
2K