The Practice of Statistics Third Edition Chapter 7: Random Variables Copyright © 2008 by W. H. Freeman & Company Daniel S. Yates

Combining RandomVariables Activity 7C Page 492

Linda Sells Cars & Trucks Linda’s cars Linda’s trucks Find If she expects to earn $350 for each car and $400 for each truck, find her expected mean earnings.

Since variance is the average of squared deviations from the mean, multiplying X by a constant b multiplies the variance by square of the constant. Adding a constant a to a random variable changes its mean but does not change its variability

Because the square of -1 is 1…

Be aware… standard deviations do not generally add. Use the rules for variance to find combined standard deviations.

Tri-State Pick 3 Find the mean and standard deviation of the game. What is the mean amount you win if each ticket costs $1.

Tri-State Pick 3 What is the mean, variance, and standard deviation of the total payoff if you buy two tickets on two different days? Notice variances of independent random variances add; standard deviations do not.

SAT scores A college uses SAT scores as one criterion for admission. Experience has shown that the distribution of SAT scores among its entire population of applicants is such that What is the mean and standard deviation of the total score X + Y among students applying to this college?

Normal calculations & combining means Any linear combination of independent Normal random variables is also Normally distributed. That is, if X and Y are independent Normal random variables and a and b are any fixed numbers, aX + bY is also Normally distributed. (Basically we can use Normal calculations with combined means and variance as well)

A Round of Golf Combining Random Variables Tom and George are playing in the club golf tournament. Their scores vary as they play the course repeatedly. Tom’s score X has the N(110, 10) distribution, and George’s score Y varies from round to round according to the N(100, 8) distribution. If they play independently, what is the probability that Tom will score lower than George and thus do better in the tournament? A. Is the difference in their means Normally distributed?

A Round of Golf Combining Random Variables Tom and George are playing in the club golf tournament. Their scores vary as they play the course repeatedly. Tom’s score X has the N(110, 10) distribution, and George’s score Y varies from round to round according to the N(100, 8) distribution. If they play independently, what is the probability that Tom will score lower than George and thus do better in the tournament? B.Find the mean and standard deviation of the difference in the scores. (Identify the parameters of the distribution of X-Y.)

A Round of Golf Combining Random Variables Tom and George are playing in the club golf tournament. Their scores vary as they play the course repeatedly. Tom’s score X has the N(110, 10) distribution, and George’s score Y varies from round to round according to the N(100, 8) distribution. If they play independently, what is the probability that Tom will score lower than George and thus do better in the tournament? C. Given N(10, 12.8), find P(X<Y)

Another example? 7.42