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Results tagged with probability
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user 207276
A probability provides a quantitative description of the likely occurrence of a particular event.
3
votes
Accepted
Compute $P\left(\int_0^1W(t)dt>\frac{2}{\sqrt3}\right)$ where $W(t)$ is a Wiener process
Now you can compute your probability using the standard normal CDF $\Phi$:
$$\begin{aligned}
& P\left(\int_0^1 W_s ds > \frac{2}{\sqrt{3}}\right)\\
& = P\left(Z \frac{1}{\sqrt{3}}> \frac{2}{\sqrt{3}}\right …
- 698
2
votes
How to prove this identity assuming Gaussian distribution?
Since $Y-F$ and $F$ are jointly gaussian, then $Y = (Y-F) + F$ is also gaussian.
You can compute the moments from the moments of $Y-F$ and $F$, or using the tower property:
For the mean:
$$\mathbb{ …
- 698