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Let Y1, Y2, Y3,... Yn be independent standard normal random variables. a What is the
Chapter 9, Problem 9.24(choose chapter or problem)
QUESTION:
Let \(Y_{1}, Y_{2}, Y_{3}, \ldots Y_{n}\) be independent standard normal random variables.
a. What is the distribution of \(\sum_{i=1}^{n} Y_{i}^{2}\) ?
b Let \(W_{n}=\frac{1}{n} \sum_{i=1}^{n} Y_{i}^{2}\). Does \(W_{n}\) converge in probability to some constant? If so, what is the value of the constant?
Questions & Answers
QUESTION:
Let \(Y_{1}, Y_{2}, Y_{3}, \ldots Y_{n}\) be independent standard normal random variables.
a. What is the distribution of \(\sum_{i=1}^{n} Y_{i}^{2}\) ?
b Let \(W_{n}=\frac{1}{n} \sum_{i=1}^{n} Y_{i}^{2}\). Does \(W_{n}\) converge in probability to some constant? If so, what is the value of the constant?
ANSWER:Step 1 of 3
Let are independent standard normal Random variables.
Therefore,