Value-at-Risk Theory and Practice

The first advanced book on value-at-risk

Chapter 3, Page 113
Exercise 4

Consider the random variable W = Z2 , where Z is defined as in the previous exercise.

a. Calculate the mean of W.

b. Calculate the variance of W.

c. Calculate the standard deviation of W.

Solution

In the following solution, denotes the PDF of Z.

a. By [3.6],

 [s1]

[s2]
[s3]
[s4]
[s5]
[s6]

b. By [3.6] and [3.7],

 [s7]

[s8]
[s9]
[s10]
[s11]
[s12]
[s13]
[s14]

c. The standard deviation of a random variable is simply the square root of its variance:

[s15]

 
 

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