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

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In summary, the formula for calculating E(x^2) for a sample of I.I.D. N(0,1) random variables is E(x^2) = Var(x) + E(x)^2. I.I.D. stands for independently and identically distributed, while N(0,1) refers to a normal distribution with a mean of 0 and a standard deviation of 1. To calculate E(x^2) for a sample, you would take the sum of each x^2 value and divide it by the total number of values. The expected value of x^2 for I.I.D. N(0,1) random variables is always 1, as the formula simplifies to 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?
 

What is the formula for calculating E(x^2) given I.I.D. N(0,1) random variables?

The formula for calculating E(x^2) given I.I.D. N(0,1) random variables is E(x^2) = Var(x) + E(x)^2.

What does I.I.D. N(0,1) mean?

I.I.D. stands for independently and identically distributed, while N(0,1) refers to a normal distribution with a mean of 0 and a standard deviation of 1. This means that each random variable has the same distribution and is not influenced by any other variables.

How do you calculate E(x^2) for a sample of I.I.D. N(0,1) random variables?

To calculate E(x^2) for a sample of I.I.D. N(0,1) random variables, you would take the sum of each x^2 value in the sample and divide it by the total number of values in the sample.

What is the expected value of x^2 for I.I.D. N(0,1) random variables?

The expected value of x^2 for I.I.D. N(0,1) random variables is 1, as the formula E(x^2) = Var(x) + E(x)^2 simplifies to 1 + 0^2 = 1.

How does the expected value of x^2 change as the number of I.I.D. N(0,1) random variables increases?

As the number of I.I.D. N(0,1) random variables increases, the expected value of x^2 stays the same at 1. This is because the formula for calculating E(x^2) takes into account the standard deviation and mean, which remain constant for I.I.D. random variables.

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