Math for Quantitative Finance
# Confidence and Estimation

Your friend believes that stock prices are normally distributed. He says that the price of Stock A at the end of the year is approximately normally distributed with mean 200 and standard deviation 40, and the price of Stock B at the end of the year is approximately normally distributed with mean 180 and standard deviation 30.

According to his hypothesis, what is the approximate probability that stock B finishes the year with a higher price than stock A?

**confidence interval**. When estimating some population parameter via sampling, a confidence interval is an interval that should contain the true parameter some percentage of the time. For example, a 90% confidence interval should contain the true parameter 90% of the time.

A stock’s (daily) log-returns are normally distributed, and a quantitative analyst finds that the 95% confidence interval for the sum of the returns over a 10 day period is \([-1,1].\)

If the stock is currently $100, then the 95% confidence interval for where it will be after these 10 trading days is \([a,b].\) What is \(a+b?\)

Note that the log-return between day \(i\) with price \(S_i\) and day \(j\) with price \(S_j\) is \(\log\left(\frac{S_j}{S_i}\right).\)

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