Mam proces Wienera. Jak obliczyć:
a) \(\displaystyle{ P\left( W_4>W_2>0\right)}\)
b) \(\displaystyle{ P\left( W_{10} ^2 + \left( W_10 - W_5\right)^2>\sqrt{2} \right)}\)
W a) próbowałam tak:
\(\displaystyle{ P\left( W_4>W_2>0\right)=P\left( W_4-W_2>0\right)=P\left(W_2>0\right)= \frac{1}{2}}\)
Natomiast jedyne co zrobiłam w b) to:
\(\displaystyle{ P\left( W_{10} ^2 + \left( W_{10} - W_5\right)^2>\sqrt{2} \right)=P\left( W_{10} ^2 + \left( W_5\right)^2>\sqrt{2} \right)}\)