Econ 41 (Winter 2015) Department of Economics, UCLA Instructor: Shuyang Sheng Midterm Exam (A) Th sh is ar stu ed d vi y re aC s ou ou rc rs e eH w...

https://www.coursehero.com/file/12661687/midterm-15W/ This study resource was shared via CourseHero.com Econ 41 (Winter 2015) Department of Economics, UCLA Instructor: Shuyang Sheng Midterm Exam (A) Each question in this exam has only one correct answer. You will get 1 credit if your choice is correct and 0 credit otherwise. Please write down the version of your exam (i.e., A, B or C) on your scantron. If the version of your exam is missing, your scantron will be graded three times (by assuming it was A, B or C respectively), and your grade of the exam will be the lowest one among the three.

1 https://www.coursehero.com/file/12661687/midterm-15W/ This study resource was shared via CourseHero.com1. Suppose that Aand Bare two events with P(A ) = 0 :3 , P (B ) = 0 :4 , and P(A [B) = 0 :5 .

(1) What is the probability of A0 ?

(a) 0:5 (b)0:6 (c)0:7 (d)0:8 (2) What is the probability of A\B0 ?

(a) 0:1 (b)0:2 (c)0:3 (d)0:4 (3) What is the probability of A0 \ B0 ?

(a) 0:1 (b)0:2 (c)0:4 (d)0:5 (4) What is the probability of A0 [ B0 ?

(a) 0:5 (b)0:7 (c)0:8 (d)0:9 2. Three di¤erent economics books, two di¤erent mathematics books, and one physics book are to be arranged on a bookshelf.

(5) How many arrangements are possible if the books in each sub ject must all stand together? (a)12 (b)24 (c)36 (d)72 (6) How many arrangements are possible if the economics books must stand together? (a)24 (b)36 (c)144 (d)288 (7) How many arrangements are possible if the economics books must stand together and to the left of the mathematics and physics books?

(a)18 (b)36 (c)72 (d)144 (8) How many arrangements by sub ject are possible if each book is labeled E (economics), M (mathemtics), or P (physics)?

(a)20 (b)60 (c)180 (d)360 3. Draw two balls at random from an urn with 6 red balls and 4 white balls. Suppose that the balls are drawn without replacement .

(9) What is the probability of drawing one red ball and one white ball? (a)4=15 (b)8= 15 (c)6= 25 (d)12=25 (10) What is the probability of drawing at least one red ball? (a)12=25 (b)21=25 (c)8=15 (d)13=15 2 https://www.coursehero.com/file/12661687/midterm-15W/ This study resource was shared via CourseHero.com(11) Given that the …rst ball is red, what is the probability that the second ball is also red?

(a)5=9 (b)4=9 (c)2= 3 (d)3=5 (12) Given that at least one ball is red, what is the probability that both balls are red? (a)3=7 (b)4=7 (c)5= 13 (d)8= 13 Now suppose that the balls are drawn with replacement.

(13) What is the probability of drawing at least one white ball?

(a)2=3 (b)2=5 (c)3= 5 (d)16=25 (14) Given that at least one ball is white, what is the probability that both balls are white? (a)1=4 (b)3=4 (c)1= 5 (d)4= 5 4. A senior student ma joring in economics is trying to decide on the number of …rms to which she should apply. Given her work experience and grades, she can expect to receive a job o¤er from 60%of the …rms to which she applies. Firms make job o¤ers independently. Suppose that the student decides to apply to three …rms.

(15) What is the probability that she receives no job o¤ers? (a)8=125 (b)24=125 (c)27=125 (d)36=125 (16) What is the probability that she receives at least one o¤er? (a)36=125 (b)81=125 (c)98=125 (d)117=125 (17) What is the probability that she receives at least two o¤ers? (a)36=125 (b)54=125 (c)81=125 (d)117=125 (18) What is the probability that she receives three o¤ers? (a)8=125 (b)24=125 (c)27=125 (d)36=125 5. Suppose that Xis a random variable with p.m.f. f(x ) = c 2 ( x + 1) 2 and support S= f0 ;1 ;2 g.

(19) What is the value of cso that f(x ) is a valid p.m.f.?

(a) 1= 14 (b)1= 7 (c)2=7 (d)1= 3 (20) What is P(X 1)?

(a) 1= 14 (b)2= 7 (c)5=14 (d)2= 3 3 https://www.coursehero.com/file/12661687/midterm-15W/ This study resource was shared via CourseHero.com Powered by TCPDF (www.tcpdf.org)(21) What is the mean of X?

(a) 11=7 (b)13=7 (c)13=14 (d)1 (22) What is the variance of X?

(a) 9=7 (b)19=49 (c)20=7 (d)38=49 (23) Let Y= 2 X 1. What is the expectation of Y?

(a) 6=7 (b)1 (c)13=7 (d)15=7 (24) What is the variance of Y?

(a) 38=49 (b)76=49 (c)20=7 (d)40=7 6. Let X 1; X 2; : : : ; X 10be 10independent random variables drawn from a distribution with support S= f 1;0 ;2 g and p.m.f. f(x ) = 1 3 for any x2 S. Let X = 1 10 P 10 i =1 X ibe the sample mean.

(25) What is the expectation of X 1?

(a) 1= 3 (b)0 (c) 1=3 (d)2=3 (26) What is the expectation of X ?

(a) 0 (b)1= 3 (c)5=3 (d)10=3 (27) What is the expectation of X 2 ? (Hint: E(X iX j) = E(X i) E (X j) if X iand X jare independent.) (a)1= 6 (b)1= 10 (c)2=5 (d)4=15 (28) What is the variance of X ?

(a) 7= 45 (b)4=15 (c)1=6 (d)1=18 4