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Unit 6 Random Variables 6.2B Combining Random Variables (with the help of MEGA Algebra) ο Describe the measures of center (mean) and spread (stdev) that result from combining two or more random variables (Combining = adding/subtracting!) Speed Dating At a speed-dating event, women sit in a circle, and each man spends about 5 minutes getting to know a woman before moving on to the next one. What is the probability that the man is taller than the woman in a randomly selected speed-dating couple? Mythical College Main Campus X 12 13 14 15 16 17 18 P(X) 0.25 0.10 0.05 0.30 0.10 0.05 0.15 Mythical College Downtown Campus Y 12 13 14 15 16 17 18 P(Y) 0.35 0.15 0.10 0.20 0.05 0.05 0.10 Consider the random variables X and Y each with its own measures of center and spread. Variable Mean X ππ Y ππ Variance Stdev ππ 2 ππ ππ 2 ππ Now consider the NEW random variable formed when we add(or subtract) values of X and Y. Letβs call this variable X ± Y. Letβs find the mean and standard deviation of X ± Y. First we will find the mean ππ±π ππ±π = ππ ± ππ Yay. Not so bad. Next we will find ππ±π by finding the variance 2 ππ±π ππ±π 2 2 = ππ +ππ 2 NOTE#1 This is only true when X & Y are independent NOTE#2 When independent, variances add, even when we subtract to get our new var. EX 1) Letβs take a random American hetero couple, calculate their heights and subtract. The NEW random variable formed would be the difference M β F. Find the mean and standard deviation of M β F. EX 2) Take two random American women, calculating their heights and subtract. The NEW random variable formed would be the difference F1 β F2. Find the mean and standard deviation of F1 β F2. Roulette Revisted ο Suppose the gambler plays two games of roulette, still keeping the $1 bet each time. What can we say about the total gain (or loss) from playing two games?