The Pareto distribution has cdf f(x) = 1 (/(x+))^. Suppose that a random variable X has a distribution which is a two-point mixture of two Pareto distributions, one with = 2, = 50, and p = 0.8, and the other with = 4, = 1250, and p = 0.2. Calculate the expected value of X. Hint: expected value of mixed distributions is pE[Y]+(1-p)E[Z] integrate both distributions from 0 to inf to find their expected values then plugin with given p values.

1. The Pareto distribution has cdf f(x) = 1 (/(x+))^. Suppose that a random variable X has a
distribution which is a two-point mixture of two Pareto distributions, one with = 2, = 50, and p
= 0.8, and the other with = 4, = 1250, and p = 0.2. Calculate the expected value of X.
Hint:
expected value of mixed distributions is pE[Y]+(1-p)E[Z]
integrate both distributions from 0 to inf to find their expected values
then plugin with given p values