PROF HONGFALL 2012ECONOMICS 3190MIDTERM EXAMNotes: (1) This is a closed b ook/notes exam. There are 8 questions, with a total of 100points; (2) you have 75 minutes; (3) suggestion: have a look at all problems and …rstsolve the problems you feel easiest; (4) good luck!1. [10 pts] Suppose P (A) =13; P (Bc) =14; and A and B are mutually independent:Find P (ASB): Give your reasoning.2. [10 pts]. A car repair can b e performed either on time or late and either satisfactorilyor unsatisfactorily.(1) The probability of a repair being on time and satisfactory is 0.26. The probabilityof a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41.What is the probability of a repair being late and unsatisfactory?(2) If a repair is made on time, then there is a probability of 0.85 that it is satisfactory.There is a probability of 0.77 that a repair will be made on time. What is the probabilitythat a repair is made on time and is satisfactory?Give your reasoning.3. [15 pts] Suppose B1; B2; and B3are mutually exclusive. If P (B1) = P (B2) =P (B2) =13and P (AjB1) =16; P (AjB2) =13; and P (AjB3) =12: Find P (A): Give yourreasoning.4. [10 pts] A three member-committee will be selected from four undergraduates andtwo graduate students. Suppose the selection is made randomly, what is the probabilitythat there will be no graduate students on the committee? Give your reasoning.5. [10 pts] An investment …rm o¤ers its customers municipal bonds that mature aftervarying numbers of years. Given the cumulative distribution of X; the number of years1to maturity for a randomly selected bond isF (x) =8>>>>>><>>>>>>:0 x < 1141  x < 3123  x < 5345  x < 71 x  7:Find the probability mass function f(x): Give your reasoning.6. [15 pts] A market research group specializes in providing assessments of the prospectsof sites for new clothing stores in shopping centers. The group assesses prospects aseither good, fair or poor. The records of requests for assessments made to this groupwere examined, and it was found that for all stores that turned out to be successful,the assessment was good for 60%, fair for 30%, and poor for 10%. For all stores thatturned out to be unsuccessful, the assessment was good for 10%, fair for 30%, and poorfor 60%. It is also known that 70% of new clothing stores are successful and 30% areunsuccessful.(1) For a randomly chosen store, what is the probability that prospects will beassessed as good?(2) If prospects for a store are assessed as good, what is the probability that it willbe successful?Give your reasoning.7. [10 pts] Suppose X has a probability density functionf(x) =(cejxj1 < x < 10 otherwise.Find the value of constant c: Give your reasoning.8. [20 pts] Suppose (X; Y ) have a joint uniform probability density functionf(x; y) =(cxeyfor 0 < x < y < 10 otherwiseFind:(1) the value of constant c;2(2) the marginal pdf fY(y);(3) the conditional pdf fY jX(yjx):(4) Are X and Y independent?Give your reasoning for all