$T_n=\Sigma_{j=1}^n Y_j$ is a symmetric simple random walk with $P(Y_j=1)=\frac{1}{2}, P(Y_j=-1)=\frac{1}{2}$ and $T_0=0$. Define $M=\mbox{min}\{i:|T_i|=n\}$. We are require to find $\mathbb{E}(M)$ and $\mathbb{E}(M^2)$.
My thought: We can have $\mathbb{E}(Y_j)=0$ and $\operatorname{Var}(Y_j) = 1$. Also $\mathbb{E}(T_n)=0$ and $\operatorname{Var}(T_n)=n$. But how to calculate $\mathbb{E}(M)$ and $\mathbb{E}(M^2)$. Please help.