In: Statistics and Probability
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: μ1 = 115;
σ1 = 8
Gary, x2: μ2 = 100;
σ2 = 18
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. (Round your answers to one decimal place.)
μ | |
σ2 | |
σ |
(b) The average of their scores is
W = 0.5x1 + 0.5x2.
Compute the mean, variance, and standard deviation for the random variable W. (Round your answers to one decimal place.)
μ | |
σ2 | |
σ |
(c) The tournament rules have a special handicap system for each
player. For Norb, the handicap formula is
L = 0.8x1 − 12.
Compute the mean, variance, and standard deviation for the random variable L. (Use 2 decimal places.)
μ | |
σ2 | |
σ |
(d) For Gary, the handicap formula is
L = 0.85x2 − 5.
Compute the mean, variance, and standard deviation for the random variable L. (Use 2 decimal places.)
μ | |
σ2 | |
σ |