Problem with Wigner matrix

Question

My problem: In the following, all the variables considered $X_{i j}, X_{i j}^{(k)}$ are:

1. i.i.d. centered with variance 1 and fourth finite moment for $i \leq j$.
2. We set $X_{i j}=\overline{X_{j i}}, X_{i j}^{(k)}=\overline{X_{j i}^{(k)}}$ for $i>j$ .

Let $X$ be a Wigner matrix: $X=\left(X_{i j}\right)_{1 \leq i, j \leq n}$.

(a) Give the asymptotic behavior of the spectral measurement of $V=\sigma \frac{X}{\sqrt{n}}$.

(b) of $\lambda_{\max }(V)$,

(c) of $\lambda_{\min }(V)$.

My attempt: I think that $\lambda_{\max }(V) \xrightarrow[n \rightarrow \infty]{\text { p.s. }} 2 \sigma \text { and } \lambda_{\min }(V) \xrightarrow[n \rightarrow \infty]{\text { p.s. }}-2 \sigma \text {. }$

But I don't know how to deal with the first problem.