I have issue resolving this exercise :
If $W_t$ is a Brownian motion we define $(X_t)_{t \ge 0}$ such that
$$ X_t= \begin{cases} W_t & \text{if } \forall s\le t, W_s>-1, \\ -1 & \text{otherwise}. \end{cases} $$
Can you compute $E[X_1]$
If someone have a clue. i know this is related to stopping time and Doob theorem maybe. Thanks in advance.