Let X denote the temperature (degree C) and let Y denote thetime in minutes that it takes for the diesel engine on anautomobile to get ready to start. Assume that the joint density for(X, Y) is given by fxy (x, y) = c(4x + 2y +1) ; 0 < x< 40 and 0 < y <2.
(a) Find the value of c that makes this a density.
(b) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C and it will take at least1 minute for the car to be ready to start.
(c) Find the marginal densities for X and Y.
(d) Find the probability that on a randomly selected day itwill take at least one minute for the car to be ready tostart.
(e) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C.
(f) Are X and Y independent? Explain on mathematicallybasis.

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.