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

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SUMMARY

The calculation of E(x^2) for independent and identically distributed (i.i.d.) random variables following a standard normal distribution, N(0,1), is derived using the relationship between variance and moments. Specifically, the variance of a standard normal distribution is 1, and the mean is 0. Therefore, E(x^2) can be calculated as E[X^2] = Var(X) + {E[X]}^2, resulting in E(x^2) = 1 + 0 = 1.

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James1990
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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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