Question

8) (10 points) Determine if the following are true or false. If false, explain why or give an example to counter the false statement. a) Two events are disjoint if the occurrence of one does not affect the other. b) It is not possible to get a probability of exactly 0. c) Drawing without replacement is an example of dependent events. d) It is possible to have both a disjoint event and an independent event. e) The standard deviation of a random variable can be negative. f) The mean of a random variable can be negative.

Answer 1

9 True & Two events are disjoint if P(AMB)= Excumple - Tossing a coint His not affected occurace of t. Their infesaction {Hat}30 and P(HAT) = 0

7 False are :- We can find o probababilty. Example Tossing a coin H&t event A&B respectively. The euen Anb=0 PCAMB) = 0 . © True & Probability of next pick is affected! by it previous, so without replacint is dependent. . (d) False By depenition To imp independut P(ANB) = P1A).PCB) · To be disjonit PCA MB)=0 И0 +от (со комьи в сојчh P(+) = 11, P(7)=1/ PLANT) = 0. This implies H&T are disjoint but not independ because PCMAT) + PCH).P(T) Ģ False i SiD always les b/w o to some positive values. Trime.» Excufale M. X3 11,273,16, mean = -=-2 ©