UCSB PSTAT 109 Statistics for Economics Question-Quiz 4

Problem 1

 Let Ω = [0, 1], and let P be given by P ([a, b]) = b − a. Define random variable

X to be

X = −1A + 3 . 1B ,

Where A = [0, 3/4] and B = [1/2, 1] are events in Ω.

a. Construct a probability table for random variable X.

b. Determine E[X] and E[X 2 ].

c. Determine V ar(X).

Problem 2

 The following table shows the number of students in three different degree

programs and whether they are undergraduate students or graduate students:

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 events A, B, and D:

P (A) = 0.4                           P (A ∪ D) = 0.6                   P (A ∩ C) = 0.04

P (B) = 0.2                            P (A |B) = 0.3                     P (A ∩ D) = 0.03

P (C) = 0.1

a. Compute P (D).

b. Compute P (A ∩ B).

c. Are events A and B mutually exclusive? Explain your answer.

d. Are events A and B independent? Explain your answer.

e. Are events A and C mutally exclusive? Explain your answer.