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Compute the probability under the normal distribution

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Given:
1) Invest $10,000 in Stock "ABC".
2) The daily returns are normally distributed with a mean of 0% and a standard deviation of 1%.

Questions:
1) What is the probability that tomorrow's return on investment in ABC is exactly 0.9%?
2) Conditional on making a positive return tomorrow, what is the probability you make a return of at least 1%?
3) What is the probability that tomorrow's return on your investment in ABC is somewhere between -1% and +.5%?
4) Calculate the "value at risk" for investment of $20,000 at the 95% confidence level.
5) You believe that 1% of mutual fund managers can "beat the market" and deliver a positive mean daily return of .5%, also with a standard deviation of 1%. The remaining 99% of funds cannot beat the market; they all have identical daily mean return of 0% and a standard deviation of 1%. A broker calls you and claims his fund is one that can beat the market. You follow the fund for the day and see that today it has a positive (greater than 0%) return. Use Bayes Theorem to compute the probability that this fund can actually beat the market.

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Solution Summary

The solution gives detailed steps on computing the probability under the normal distribution and the conditional probability applying Bayes theorem.

Solution Preview

1) Since the dairy returns are normally distributed, it is a continuous distribution. So the probability that tomorrow's return on investment in ABC is exactly 0.9% is zero.

2) Since ...

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