Exercise 5.3. A financial regulator from the FED will evaluate two banks this week. For each evaluation, the regulator will choose with equal probability between two different stress tests. Failing under test one costs a bank 10K fee, whereas failing test 2 costs 5K. The probability that the first bank fails any test is 0.4. Independently, the second bank will fail any test with 0.5 probability. Let X denote the total amount of fees the regulator can obtain after having evaluated both banks. Determine the cumulative distribution function of X