I wonder why here in the solution above, Why P{Y(1/2)> - segema} becomes P{ Y(1/2)/segema/ square root of2}
Thanks
2026-04-03 10:46:32.1775213192
An example with Brownian Motion
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We divide each side of the inequality by $\sigma/\sqrt{2}$, which is how we get from the first circled step to the next.
If you're asking why we're dividing, it's because we want to make the random variable on the left-hand side of the inequality a standard normal random variable. This way, we can use the normal cumulative distribution function to finish our calculation.