Expand Your Knowledge: Linear Functions and Combinations of Independent Random Variables: Golf How can we compute the mean and standard deviation of new random variables created by a linear function of one random variable or a linear combination of two independent random variables? The following discussion shows us.

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 5 115; s1 5 12 Gary, x2 :m2 5 100; s2 5 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 5 x1  x2. Compute the mean, variance, and standard deviation for the random variable W.

(b) The average of their scores is W 5 0.5x1 1 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 5 0.8x1  2.

Compute the mean, variance, and standard deviation for the random variable L.

(d) For Gary, the handicap formula is L 5 0.95x2  5.

Compute the mean, variance, and standard deviation for the random variable L.