Homework 20: Variance and Standard Deviation

1. Section 4.3, #3, 4, 6, 7(a).
2. Two distinct integers are chosen at random from the first five positive integers. Compute the expected value and variance of the absolute value of the difference of the two numbers.
3. A box contains 5 red and 5 blue marbles. Two marbles are drawn randomly. If they are the same color, then you win $1.10; if they are different colors, then you lose $1.00. Calculate the expected value and standard deviation of your winnings.
4. Suppose that teams A and B play in the world series, and that team A has a 60% chance of winning any game against team B. Find the expected value, variance, and standard deviation of the number of games that will be played. (The series is the best of seven - the first team to win four games wins the series.)
5. Let \(X\) have pdf \begin{equation*} f_X(x)= \begin{cases} 2(1-x), &\text{if }0\leq x\leq 1\\ 0, &\text{otherwise} \end{cases} \end{equation*} Find \(E(X)\), \(E(X^2)\), Var\((X)\), and Std Dev\((X)\).