課程名稱︰統計學與計量經濟學上
課程性質︰經濟系大二必修
課程教師︰張勝凱
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰2018/10/24
考試時限（分鐘）：180
試題 :
Problem 1.(15 points (7,8)
Let X have p.m.f f(x)=x/10, x= 1,2,3,4
(1) Find E(X)
(2) Find E[X(5-X)]
Problem 2.(20 points (7,7,3,3))
For the joint p.d.f. of random variables X and Y,
fxy(x,y)=x+y, 0<=x,y<=1.
(1) Find the conditional expectation function E(Y|X)
(2) Find the best linear prediction E*(Y|X)
(3) Are X and Y stochastically independent?
(4) Is Y mean independent of X?
Problem 3.(20 points (5,5,5,5))(註:考試會發常態分配表)
The monthly income of residents of Daisy City is normally
distributed with a mean of 3000 and a standard deviation
of 500.
(1) The mayor of Daisy City makes 2250 a month. What percentage
of Daisy City's residents has incomes that are more than the
mayor's?
(2) Individuals with incomes of less than 1985 per month are
exempt from city taxes. What percentage of residents is exempt
from city taxes?
(3) What are the minimum and the maximum incomes of the middle
97% of the residents?
(4) Two hundred residents have incomes of at least 4440 per month.
What is the population of Daisy City?
Problem 4. (15 points (7,8))
(1) Forty percent of the students who enroll in a statistics course
go to the statistics laboratory on a regular basis. Past data
indicates that 65% of those students who use the lab on a
regular basis make a grade of A in the course. On the other hand,
only 10% of students who do not go to the lab on a regular basis
make a grade of A. If a particular student made an A, determine
the probability that she or he used the lab on a regular basis.
(2) In a city, 60% of the residents live in houses and 40% of the
residents live in apartments. Of the people who live in houses,
20% own their own business. Of the people who live in apartments,
10% own their own business. If a person owns his or her own
business, find the probability that he or she lives in a house.
Problem 5. (10 points (5,5))
Let the joint probability mass function of random variables, X and Y
follow
fxy(x,y)=(x+y)/27, where x=0,1,2; y=1,2,3
(1) Compute E(Y|X=x)
(2) Compute E(7+6Y|X=2)
Problem 6. (12 points (3,3,3,3))
Let X is a continuous random variable, and
fx(x)={c, 0<=x<=4
0, otherwise
(1) Find c
(2) Compute E(2X+5)
(3) Find the c.d.f. Fx(x)
(4) Compute P(1<=X<=3)
Problem 7. (8 points)
Let Z=E(Y|X) and we know that Cov(Y,Z)=0. Find Var(Z)