Let X be N(0, 1). Use the mgf technique to show that Y = X2 is 2(1). Hint: Evaluate the

Chapter 5, Problem 5.4-23

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QUESTION:

Let X be N(0, 1). Use the mgf technique to show that \(Y = X^2\) is \(\chi^{2}(1)\). Hint: Evaluate the integral representing \(E\left(e^{t X^{2}}\right)\) by writing \(w=x \sqrt{1-2 t}\).

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QUESTION:

Let X be N(0, 1). Use the mgf technique to show that \(Y = X^2\) is \(\chi^{2}(1)\). Hint: Evaluate the integral representing \(E\left(e^{t X^{2}}\right)\) by writing \(w=x \sqrt{1-2 t}\).

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Definition. Moment generating function (mgf), denoted by , of a random variable  is defined by

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