1.
| \(x\) | \(\Pr(X = x)\) |
|---|---|
| 1 | 0.1 |
| 2 | 0.05 |
| 3 | 0.2 |
| 4 | 0.15 |
| 5 | 0.15 |
| 6 | 0.1 |
| 7 | 0.05 |
| 8 | 0.1 |
| 9 | 0.1 |
Section 3.2 Variance
Text of section.
Exercises Exercises
2.
Let \(X\) be a random variable taking the values 1, 2, 3, 4, 5. Write a distribution table for \(X\text{,}\) then use your table to write a distribution for \(X^2\text{.}\) Then, find \(\Var(X)\text{.}\)
3.
Suppose we flip a coin \(n = 100\) times, and let \(N\) count the number of heads. If the coin comes up heads on a flip with probability \(p = 0.4\text{,}\) what is \(\Var(N)\text{?}\) What if \(n = 80\) and \(p = 0.6\text{?}\) What if \(n = 200\) and \(p = 0.5\text{?}\)
4.
5.
A continuous random variable \(X\) taking values in \([0, 1]\) has p.d.f. \(f(x) = 2x\text{.}\) What is \(\Var(X)\text{?}\)
6.
A continuous random variable \(X\) taking values in \([-1, 1]\) has p.d.f. \(f(x) = \frac{3x^2}{2}\text{.}\) What is \(\Var(X)\text{?}\)
7.
A continuous random variable \(X\) taking values in \([1, 4]\) has p.d.f. \(f(x) = \frac{4}{3x^2}\text{.}\) What is \(\Var(X)\text{?}\)
8.
A continuous random variable \(X\) taking values in \([1, 4]\) has p.d.f. \(f(x) = k(x - \sqrt{x})\) for some constant \(k\text{.}\) In a previous problem, you found the value of \(k\text{.}\) Now, find \(\Var(X)\text{.}\)
9.
A continuous random variable \(X\) taking values in \([1, 2]\) has p.d.f. \(\displaystyle{f(x) = \frac{1}{2}\left(\frac{1}{x^2} + x\right)}\text{.}\) Find \(\Var(X)\text{.}\)
