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[Learn more about Teams](https://stackoverflow.co/teams/) # [An example with Brownian Motion](https://math.stackexchange.com/questions/3604197/an-example-with-brownian-motion) [Ask Question](https://math.stackexchange.com/questions/ask) Asked 5 years, 4 months ago Modified [5 years, 4 months ago](https://math.stackexchange.com/questions/3604197/an-example-with-brownian-motion?lastactivity "2020-04-01 01:37:41Z") Viewed 206 times 1 \$\\begingroup\$  I wonder why here in the solution above, Why P{Y(1/2)\> - segema} becomes P{ Y(1/2)/segema/ square root of2} Thanks - [probability](https://math.stackexchange.com/questions/tagged/probability "show questions tagged 'probability'") - [stochastic-processes](https://math.stackexchange.com/questions/tagged/stochastic-processes "show questions tagged 'stochastic-processes'") - [markov-chains](https://math.stackexchange.com/questions/tagged/markov-chains "show questions tagged 'markov-chains'") - [brownian-motion](https://math.stackexchange.com/questions/tagged/brownian-motion "show questions tagged 'brownian-motion'") [Share](https://math.stackexchange.com/q/3604197 "Short permalink to this question") Cite Follow [edited Apr 1, 2020 at 1:37](https://math.stackexchange.com/posts/3604197/revisions "show all edits to this post") [](https://math.stackexchange.com/users/38296/jeel-shah) [Jeel Shah](https://math.stackexchange.com/users/38296/jeel-shah) 9,5702121 gold badges8080 silver badges126126 bronze badges asked Apr 1, 2020 at 0:21 [](https://math.stackexchange.com/users/764315/cynthiaaaaii) [cynthiaaaaii](https://math.stackexchange.com/users/764315/cynthiaaaaii)cynthiaaaaii 2144 bronze badges \$\\endgroup\$ 1 - 1 \$\\begingroup\$ Hi cynthiaaaaii, thanks for posting the question. Can you copy the text in your image to the description because this will make the problem easy to find later. \$\\endgroup\$ – [Jeel Shah](https://math.stackexchange.com/users/38296/jeel-shah "9,570 reputation") Commented Apr 1, 2020 at 1:38 [Add a comment](https://math.stackexchange.com/questions/3604197/an-example-with-brownian-motion "Use comments to ask for more information or suggest improvements. Avoid answering questions in comments.") \| ## 1 Answer 1 Sorted by: [Reset to default](https://math.stackexchange.com/questions/3604197/an-example-with-brownian-motion?answertab=scoredesc#tab-top) 2 \$\\begingroup\$ 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. [Share](https://math.stackexchange.com/a/3604233 "Short permalink to this answer") Cite Follow answered Apr 1, 2020 at 1:24 [](https://math.stackexchange.com/users/614428/ekesh-kumar) [Ekesh Kumar](https://math.stackexchange.com/users/614428/ekesh-kumar)Ekesh Kumar 3,47411 gold badge1212 silver badges2323 bronze badges \$\\endgroup\$ [Add a comment](https://math.stackexchange.com/questions/3604197/an-example-with-brownian-motion "Use comments to ask for more information or suggest improvements. Avoid comments like “+1” or “thanks”.") \| ## You must [log in](https://math.stackexchange.com/users/login?ssrc=question_page&returnurl=https%3A%2F%2Fmath.stackexchange.com%2Fquestions%2F3604197) to answer this question. Start asking to get answers Find the answer to your question by asking. 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