Sample Question #169 (probability theory)

Let *x ~ N*(0, 1). What’s the expectation and variance of *x*^{2}?

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Sample Question #169 (probability theory)

Let *x ~ N*(0, 1). What’s the expectation and variance of *x*^{2}?

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ANSWER

This is a chi-squared(1) distribution. Its mean is 1 and variance is 2.

(Bonus question: what’s the definition of a chi-squared(n) distribution? What are the expectation and variance of a chi-squared(n) distribution?)

chi(n,2n)wikipedia defn. belowIf Xi are k independent, normally distributed random variables with mean 0 and variance 1, then the random variable

is distributed according to the chi-square distribution. This is usually written