List of top Stochastic Processes Questions on Brownian Motion

Let \( \{ B(t) \}_{t \geq 0} \) be a standard Brownian motion and let \( \Phi(\cdot) \) be the cumulative distribution function of the standard normal distribution. If \[ P\left( \left( B(2) + 2B(3) \right)>1 \right) = 1 - \Phi\left( \frac{1}{\sqrt{\alpha}} \right), \, \alpha>0, \] then the value of \( \alpha \) (in integer) is equal to ________

Let \( W(t) \) be a standard Brownian motion. Then the variance of \( W(1)W(2) \) equals