Value-at-Risk

Chapter 3, Page 132
Exercise 22

Answer the following questions:

a. If U ~ U(0, 1), how is V = 1 – U distributed?

b. If U ~ U(0, 1), how is W = bU + a distributed for arbitrary constants a, b?

Solution

a. U(0,1)

b. U(a, a + b)

Note that both of these results can be obtained intuitively with a moment's thought. The results can be formally derived by calculating the respective CDFs of V and W. Use [3.4] for this purpose.