A missile protection system consists of n radar sets operating independently, each with probability 0.9 of detecting a missile entering a zone that is covered by all of the units. a) Find a nice expression for the probability of detecting at least one of the sets detects the missile. (Tip: what is the probability, that a missile is not detected by any of the sets? - and what has this probabilityto do with the above?)b) How large must n be if we require that the probability of detecting a missile that enters the zone be 0.999 ? 0.999999 ?c) If n = 5 and a missile enters the zone, what is the probability that exactly 4 sets detect the missile?At least one set?

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.