# Exercise Solution 3.40

- By [3.128], μ =
**ξ**′**μ**= 0.4. - By [3.129]
[s1]

[s2]

[s3]

- By [3.131], we seek probabilities
*q*_{1}and*q*_{2}such that[s4]

By [3.132], those probabilities must satisfy

[s5]

Combining [s4] and [s5], we seek probabilities

*q*_{1}and*q*_{2}such that[s6]

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

[s7]

Applying [3.133], we obtain the .25-quantile of

*X*as –1.598.