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Math Help - Squared Standard Normal Random Variables

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    Squared Standard Normal Random Variables

    My probability & statistics textbook states that the mean of a squared standard normal random variable is 1, but it doesn't explain how and I'm extremely confused. It seems to me that a squared standard normal random variable's mean should just be the standard normal random variable's mean squared, which would be 0^2 = 0. Can anybody help explain my error? Thanks!
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    Quote Originally Posted by lonrisbuel View Post
    My probability & statistics textbook states that the mean of a squared standard normal random variable is 1, but it doesn't explain how and I'm extremely confused. It seems to me that a squared standard normal random variable's mean should just be the standard normal random variable's mean squared, which would be 0^2 = 0. Can anybody help explain my error? Thanks!
    Your errors are several and include the error of thinking that E(X^2) = [E(X)]^2 (if this was true then the variance of all distributions would be zero).

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