Exercise Solution 3.40
- By [3.128], μ = ξ′μ = 0.4.
- By [3.129]
- By [3.131], we seek probabilities q1 and q2 such that
By [3.132], those probabilities must satisfy
Combining [s4] and [s5], we seek probabilities q1 and q2 such that
This is a two-dimensional non-linear equation. It can be solved using Newton’s method. If you are using Microsoft Excel, you can simply use the solver function (see spreadsheet). The solution is
Applying [3.133], we obtain the .25-quantile of X as –1.598.