1
Problem Set 1
Economics 103
Winter 2009
Due:
Tuesday, January 20
Beginning of class
Question 1:
True, False, Explain.
You are graded on your explanation.
1.
The probability of an outcome is the number of times that the outcome occurs in the long
run.
2.
The expected value of a discrete random variable is the outcome that is most likely to
occur.
3.
Let
Y
be a random variable. Then var(
Y
) equals
[(
)]
Y
EY
μ
−
.
4.
Two random variables
X
and
Y
are independently distributed if
.
5.
The correlation between
X
and
Y
cannot be negative since variances are always positive.
6.
To standardize a variable you add and subtract 1.96 times the standard deviation to the
variable.
7.
Assume that
Y
is normally distributed
. Moving from the mean (
) 1.64
standard deviations to the left and 1.64 standard deviations to the right, then the area
under the normal p.d.f. is 0.05.
8.
The sample average is a random variable and has a probability distribution that is the
same as for the
i.i.d. variables.
9.
If two random variables have a correlation of zero, they are independent.
10.
A probability density function tells the probability that a random variable is less than or
equal to a certain value.
11.
Econometric techniques allow us to establish a causal relationship between two variables.
12.
An estimate and an estimator are the same thing.
13.
Any linear combination of normally distributed random variables is Fdistributed.
()
[(  )
]
E
YE
E
Y
X
=
2
(, )
N
μσ
1
,...,
n
YY
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14.
The size of an 80 % confidence interval will not depend on the variance of the estimator
used to generate the confidence interval.
15.
An estimator is a formula that gives an efficient guess of the true population value.
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 Winter '07
 SandraBlack
 Economics, Normal Distribution, Standard Deviation, Variance, per capita, high school gpa

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