Question;PSTAT 109: Quiz 4;Winter 2014;Instructions: Please show all formulas and calculations in an organized fashion;for full credit.;Problem 1.Let = [0,1], and letPbe given byP([a, b]) =b????a. Dene random variable;Xto be;X=????1A+ 31B;whereA= [0,3=4] andB= [1=2,1] are events in.;a. Construct a probability table for random variableX.;b. DetermineE[X] andE[X2].;c. DetermineV ar(X).;Problem 2.The following table shows the number of students in three di;erent degree;programs and whether they are undergraduate students or graduate students;Degree Program Undergraduate GraduateTotal;Business 150 50200;Engineering 150 25175;Arts & Sciences 100 25125;Total 400 100 500;a. What is the probability that a randomly selected student is an undergraduate?;b. A student is enrolled in the Arts and Sciences school. What is the probability that;the student is an undergraduate?;c. What is the probability that a randomly selected student is a graduate Business major?;Problem 3.Suppose you are given the following information on eventsA,B, andD;P(A) = 0:4P(A[D) = 0:6P(A\C) = 0:04;P(B) = 0:2P(AjB) = 0:3P(A\D) = 0:03;P(C) = 0:1;a. ComputeP(D).;b. ComputeP(A\B).;c. Are eventsAandBmutually exclusive? Explain your answer.;d. Are eventsAandBindependent? Explain your answer.;e. Are eventsAandCmutally exclusive? Explain your answer.
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