Question

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 = 120; σ1 = 10

Gary, x2: μ2 = 110; σ2 = 9

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. (Use 1 decimal place.)
Find the:

μ:

σ2:

σ:

Answer 1

Expectation algebra is used to find the mean and variance of linear combinations of independent normal random variables.
\[E[W]=E[x _{1}]-E[x _{2}]\]
\[\mu _{w}=120-110=10\]
\[Var[W]=10^{2}+9^{2}=181\]
\[\sigma _{w}=\sqrt{181}\]