Hi everyone. I am currently in a club that prepares students for technical interviews for jobs such as investment banking, private equity and hedge funds. One of our mentors assigned us this question and to be honest I really do not have an idea how to approach it. I'm not sure if I am completely missing something that is obvious. I have not taken a math class in a couple years so I am definitely rusty.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a purely probabilistic game that you have the opportunity to play. Each time you play there are n potential known outcomes x1, x2, ..., xn (each of which is a specified gain or loss of dollars according to whether xi is positive or negative). These outcomes x1, x2, ..., xn occur with the known probabilities p1, p2, ..., pn respectively (where p1 + p2 + ... + pn = 1.0 and 0 <= pi <= 1 for each i). Furthermore, assume that each play of the game takes up one hour of your time, and that only you can play the game (you can't hire someone to play for you).

Let E be the game's expected value and S be the game's standard deviation.

1. In the real world, should a rational player always play this game whenever the

expected value E is not negative? Why or why not?

2. Does the standard deviation S do a good job of capturing how risky this game is?

Why or why not?

3. If you personally had to decide whether or not to play this game, how would

you decide?

~Rhyn

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# Risk Probability Question W/ Expected Value and Standard Deviation

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