← 1. Statistics and Probability Basics

Exercises

Problems to check your understanding of this chapter. The solutions are folded away — try them yourself first.

Easy

1EasyCompute

Returns follow a normal distribution with mean 12%12\% and volatility 20%20\%.

Find the probability that a return exceeds 32%32\%.

Distribution with mean 12%12\%, volatility 20%20\%, cutoff 32%32\%
Show solution

  1. Standardize: z=(32−12)/20=1z = (32 - 12) / 20 = 1.

  2. The exceedance probability is 1−Φ(1)≈1−0.841=0.1591 - \Phi(1) \approx 1 - 0.841 = 0.159.

Answer

About 0.1590.159, that is about 15.9%15.9\%