Problem 1.Let = [0;1], and letPbe given byP([a; b]) =b????a.

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.