Value-at-Risk Theory and Practice
The first advanced book on value-at-risk
Chapter 3, Page 158 Exercise 43
a. X ~ N(1, 4);
b. Y = 3Q + R +5, where Q ~ U(0, 1) and R ~ (2, 1) are independent;
c.
Solution
a. By [3.205]
[s1]
b. By [3.204] and [3.206]
[s2]
By [3.203]
[s4]
c. The square of a standard normal random variable is chi-squared. Specifically
[s7]
By [3.206]
[s8]
[s9]
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(2,
1) are independent; 
