# hw1_answer_econ120a_su06 - Economics 120A Professor Yongil...

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Economics 120A Name: _________________________ Professor Yongil Jeon Summer 2006 Student ID#: _________________________ Answer to Homework #1 – Summer 2006 (Answer to Midterm Exam, Summer 2005) 1-a. (3 points) The probability of an event A or B (Pr( A B )) to occur equals a. Pr( A ) × Pr( B ). b. Pr( A ) + Pr( B ) if A and B are mutually exclusive. c. Pr( ) Pr( ) A B . d. Pr( A ) + Pr( B ) even if A and B are not mutually exclusive. Answer : b 1-b. (3 points) The cumulative probability distribution shows the probability a. that a random variable is less than or equal to a particular value. b. of two or more events occurring at once. c. of all possible events occurring. d. that a random variable takes on a particular value given that another event has happened. Answer : a 1-c. (3 points) Let Y be a random variable. Then var( Y ) equals a. 2 [( ) ] Y E Y µ . b. [|( ) |] Y E Y µ . c. 2 [( ) ] Y E Y µ . d. [( )] Y E Y µ . Answer : c 1-d. (3 points) The correlation between X and Y a. cannot be negative since variances are always positive. b. is the covariance squared. c. can be calculated by dividing the covariance between X and Y by the product of the two standard deviations. d. is given by cov( , ) ( , ) var( )var( ) X Y corr X Y X Y = . Answer : c

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2 Answer to HW #1, ECON 120A, SUMMER 2006 1-e. (3 points) var( ) aX bY + = a. 2 2 2 2 X Y a b σ σ + . b. 2 2 2 2 2 X XY Y a ab b σ σ σ + + . c. XY X Y σ µ µ + . d. 2 2 X Y a b σ σ + . where 2 x σ is the variance of X and xy σ is the covariance of X and Y . Answer : b 2. (10 points) A sample of twelve Econ120A students found the following figures for number of hours spent studying the course material in the week before the final exam: 12 7 4 16 21 5 9 3 11 14 10 6 (a) (2 points) Find the sample mean. (b) (3 points) Find the sample median (c) (3 points) Find the sample variance and standard deviation (d) (2 points) Find the interquartile range (answer) (a) 8333 . 9 12 118 = = = n x x i (b) median = (9+10)/2=9.5 (c) 5152 . 28 11 333 . 1160 1474 2 = = s and s=5.34 (d) 1 st quartile = 5+(1/4)=5.25 3 rd quartile = 12+(3/4)(14-12)=13.5 interquartile range = 8.25
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