Assume that individual income is uniformly distributed between $0 and

$100,000. For each of the following, plot the estimated distribution

using simulations.

(a) Suppose individuals select their spouse completely at random.

What is the distribution of total household income in this case.

(Mathematically, what is the distribution of X +Y where X, and

Y are independent Uniform(0; 100000)?)

(b) Suppose individuals are more likely to form pairs with others of

similar income. Describe and implement at least two ways of

modeling this phenomenon. What is the impact to the distribution

of household income?