Let $(B_t)_{t\ge 0}$ be a standard Brownian Motion. Let $$T:=\inf\left\{t\ge0:B_t=5t-2\right\}$$
Calculate $E[T]$.
My teacher said as a hint that I could use the fact that $E[T]$ is finite. That would mean that according to Wald's Lemma, we know that 1. $E[B_T]=0$. Also using Wald's 2nd Lemma it is known that $E[B_T^2]=E[T]$.
How can I also express $E[B_T]$ to solve this problem?
Since $T<\infty$ a.s. and Brownian paths are continuous it follows that $B_T=5T-2$. Hence, $0=EB_T=E(5T-2)$ which gives $ET=\frac 2 5$.