Recall that \( X_{1}, \ldots, X_{n} \) are i.i.d. standard normal variables. Denote by \( A_{n} \) the sample mean of the squares of these variables:
\[
A_{n}:=\overline{X_{n}^{2}}=\frac{1}{n} \sum_{i=1}^{n} X_{i}^{2}=\frac{1}{n}\left(X_{1}^{2}+X_{2}^{2}+\ldots+X_{n}^{2}\right) .
\]
\( 2(f) \)
10 point possible (graded, results hidden)
Recall \( A_{n}=\frac{1}{n} \sum_{i=1}^{n} X_{i}^{2} \). Define a sequence of random variables \( B_{n}=e^{\mu_{n}} \).
Does the sequence of random variables \( B_{n}=e^{A_{n}} \) converge in probability to a constant \( b \) ? If yes, enter the value of \( b \) below; if no, enter "DNE".
(Enter e for the constant \( e \).
\[
B_{n} \stackrel{P}{\rightarrow} b=
\]