Combination of Random Variables: Golf Norb and Gary are

Chapter , Problem 15

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Combination of Random Variables: Golf Norb and Gary are entered in a local golf tournament. Both have played the local course many times. Their scores are random variables with the following means and standard deviations. Norb, x1: m1 115; s1 12 Gary, x2: m2 100; s2 8 In the tournament, Norb and Gary are not playing together, and we will assume their scores vary independently of each other. (a) The difference between their scores is W x1 x2. Compute the mean, variance, and standard deviation for the random variable W. (b) The average of their scores is W 0.5x1 0.5x2. Compute the mean, variance, and standard deviation for the random variable W. (c) The tournament rules have a special handicap system for each player. For Norb, the handicap formula is L 0.8x1 2. Compute the mean, variance, and standard deviation for the random variable L. (d) For Gary, the handicap formula is L 0.95x2 5. Compute the mean, variance, and standard deviation for the random variable L. 1

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