Solution Found!
Let Y1, Y2, Y3, . . . Yn be independent standard normal
Chapter 9, Problem 24E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) be independent standard normal random variables.
a What is the distribution of \(\sum_{i=1}^{n} Y_{1}^{2}\)?
b Let \(W_{n}=\frac{1}{2} \sum_{i=1}^{n} Y_{1}^{2}\). Does \(W_{n}\) converge in probability to some constant? If so, what is the value of the constant?
Equation Transcription:
Text Transcription:
Y_1, Y_2, …., Y_n
sum_{i=1}^{n} Y_{1}^{2}
W_n = frac{1}{2} sum_{i=1}^{n} Y_{1}^{2}
W_n
Questions & Answers
QUESTION:
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) be independent standard normal random variables.
a What is the distribution of \(\sum_{i=1}^{n} Y_{1}^{2}\)?
b Let \(W_{n}=\frac{1}{2} \sum_{i=1}^{n} Y_{1}^{2}\). Does \(W_{n}\) converge in probability to some constant? If so, what is the value of the constant?
Equation Transcription:
Text Transcription:
Y_1, Y_2, …., Y_n
sum_{i=1}^{n} Y_{1}^{2}
W_n = frac{1}{2} sum_{i=1}^{n} Y_{1}^{2}
W_n
ANSWER:Step 1 of 3
(a)
denotes a random sample of size from a normal distribution with mean and variance 1 .