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

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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.
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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.
 
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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?
 

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