Derive the characteristic function for the beta distribution XXXXXXXXXXand hence, or otherwise, verify XXXXXXXXXX). For the double-exponential distribution XXXXXXXXXXderive the characteristic function...

Derive the characteristic function for the beta distribution (1.5.61) and hence, or otherwise, verify (1.5.62).

For the double-exponential distribution (1.5.63) derive the characteristic function and verify (1.5.64).

Show that the characteristic function of the Cauchy distribution does not satisfy the condition for the existence of its firs two moments.

Chapter 2