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