REVIEW Example 8 0 with probability 1 with probabilit Defi Zn =l-z for all n n have the same distribution. Zn→Z 0 weber regardless of the vvalue of Z. So, Zn does not converge in p robability to Z (P(Zn-2|>)=P(|Zn-2=1)=1)REVIEW 5 Example 8 Z =
0 with probability 1 2 1 with probability 1 2 Define Zn = 1 − Z for all n. Since all the Zn have the same distribution, Zn d→ Z. However, |Zn − Z| = |1 − 2Z| = 1 regardless of the value of Z. So, Zn does not converge in probability to Z. (P (|Zn − Z| > ε) = P (|Zn − Z| = 1) = 1)