1. MGMT 322 T UTORIAL 4 QUIZ 4 2013-11-14

2. Q UESTION 1 A) Define Statistically Dependent and Independent Events. B) Give 2 examples for independent events and explain why these 2 events are statistically independent. C) Give 2 examples for dependent events and explain why these 2 events are statistically dependent.

3. Q UESTION 1 Statistically Independent Events Two events are said to be independent of each other in statistical sense only if the probability of occurrence of an event is not affected by (or dependent upon) the occurrence of the other event. Example Events: A: Siroos goes to IRAN next Tuesday B: Istanbul stock market decreases by more than 10% next Friday. Therefore: Event A and B are Independent events because the occurrence of event “A” does not have an impact on the probability of the occurrence of event “B”.

4. Q UESTION 1 Statistically Dependent Events Two events are said to be dependent events if the probability of the occurrence of an event is affected by (or dependent upon) the occurrence of the other event. Example Events: A: Stock Market Index rises tomorrow B: Interest rates go down today Therefore: Event A and B are Dependent because the occurrence of event “B” is expected to increase the probability of the event “A

5. Q UESTION 2 If events A and B are independent How can we obtain joint probability of these two events How can we obtain probability of event A given that event B occurs? Note: Just write the formula that you need to use in each case

6. Q UESTION 2 A) P(AB) = P(A) * P(B) P(BA) = P(B) * P(A) B) P(A/B) = P(A) A and B are independent events.

7. Q UESTION 3 The probability of this year’s growth rate of Turkey to be more than 5% is 0.20 and the probability of Barcelona winning this year’s champions league is 0.4 A) Calculate the joint probability of these two events. B) Probability of Turkey’s growth to be more than 5% if Barcelona wins champions league. C) Probability of Turkeys growth rate to be less than or equal to 5% if Barcelona wins this year’s champions league

8. Q UESTION 3 A) Events: G: this year’s growth rate of Turkey to be more than 5% W: Barcelona winning this year’s champions league joint probability: P(GW)= P(G)P(W)= 0.4*0.2 =0.08

9. Q UESTION 3 B) P(G/W)= P(G)= 0.2 C) L: Turkeys growth rate to be less than or equal to 5% P(L/W)= P(L)= 1-0.2= 0.8