Solution Found!
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(choose chapter or problem)
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 \(w=x \sqrt{1-2 t}\).
Questions & Answers
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 \(w=x \sqrt{1-2 t}\).
ANSWER:Step 1 of 3
Definition. Moment generating function (mgf), denoted by , of a random variable is defined by