Let Y1, Y2, Y3, . . . Yn be independent standard normal

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