# Exercise Solution 4.21

To calculate *E*(* ^{t}X*), we start with [4.53]:

[4.53]

Taking the unconditional expectation of both sides, we obtain

[s1]

[s2]

[s3]

[s4]

To calculate ^{t–1}*E*(* ^{t}X*), we again start with [4.53]:

[4.53]

Taking the conditional expectation of both sides, we obtain

[s5]

[s6]

[s7]

[s8]