Econ 210 Fruehling Quarter 2009
Problem Set 4  Solutions
1.
TRUE/FALSE
a.
The sample mean is a random variable
TRUE. It varies from sample to sample and is constructed from random variables.
b.
One drawback of the sample median is that it is very sensible to the inclusion of
outliers in the sample.
FALSE. It is the sample mean (not median) that is sensitive to outliers.
c.
Consider X~N(5,100). The interquartile range is equal to 1.35
FALSE. P(X<a)=.25
=>
5
0.25
10
a
P
Z
−
⎛
⎞
<
=
⎜
⎟
⎝
⎠
. We know that P(Z<0.675)=.25. This
means that 1P(Z<0.675)=0.75. Solving
1
1
5
0.675
1.75
10
a
a
−
= −
⇒
= −
and
2
2
5
0.675
11.75
10
a
a
−
=
⇒
=
. So the IQR= 13.5.
d.
Let X follow a Chisquared distribution with 5 degrees of freedom. Then
P(X<11)=0.99
FALSE. The critical value such that 1% of the distribution lie to the right is 15.09
2.
Calculate the following Probabilities
a.
If Y~N(2,4) calculate Pr(Y<3) = 0.6915
b.
If Y~N(4,9) calculate Pr(Y>0)
= .9082
c.
If Y~N(8,2) calculate Pr(6<Y<8)
=
.4207
d.
If Y~N(8,2) calculate Pr(8>Y>6) = .4207
3.
What does i.i.d mean? Explain using an example.
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 Winter '09
 Pavan
 Normal Distribution, Standard Deviation, 1%, 4%, 3%

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