91Ó°ÊÓ

Find the expected value of each random variable: a) \(\begin{array}{l|l|l|l}x & 10 & 20 & 30 \\\\\hline P(X=x) & 0.3 & 0.5 & 0.2\end{array}\) b) \(\begin{array}{l|c|c|c|c}x & 2 & 4 & 6 & 8 \\\\\hline P(X=x) & 0.3 & 0.4 & 0.2 & 0.1\end{array}\)

A coffee shop tracks sales and has observed the distribution in the following table. What is the average daily sales that it can expect? $$\begin{array}{|l|l|l|l|l|l|}\text { # of Sales } & 145 & 150 & 155 & 160 & 170 \\\\\hline \text { Probability } & 0.15 & 0.22 & 0.37 & 0.19 & 0.07\end{array}$$

You roll a die. If it comes up a \(6,\) you win \(\$ 100 .\) If not, you get to roll again. If you get a 6 the second time, you win \(\$ 50 .\) If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What would you be willing to pay to play this game?

Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: $$\begin{array}{cc|c} & \text { Mean } & \text { SD } \\\\\hline X & 10 & 2 \\\Y & 20 & 5\end{array}$$ a) \(3 X\) b) \(Y+6\) c) \(X+Y\) d) \(X-Y\) e) \(X_{1}+X_{2}\)

A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of \(11 .\) Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?