## Probability and Computing: Chapter 3 Exercises

Exercise 3.2: Let $X$ be a number chosen uniformly at random from $[-k,k]$. Find $Var[X]$.

Exercise 3.7: A simple model of the stock market suggests that, each day, a stock with price $q$ will increase by a factor $r>1$ to $qr$ with probability $p$ and will fail to $\frac{q}{r}$ with probability $1-p$. Assuming we start with a stock with price $1$, find a formula for the expected value and the variance of the price of the stock after $d$ days.

Exercise 3.10: For a geometric random variable $X$, find $E[X^{2}]$ and $E[X^{4}]$. (Hint: Use the lemma 2.5)

Exercise 3.12: Find an example of a random variable with finite expectation and unbound variance.Give a clear argument showing that your choice has these properties.

Exercise 3.13: Find an example of a random variable with finite $j$th moments for $1 \leq j \leq k$ but an unbound $(k+1)$th moment. Give a clear argument showing that your choice has these properties.

### 3 responses to this post.

1. fuck, you have no answers!