2008 August 16 (1:00 PM – 4:00 PM)
General Instructions:
1. You may use only pens with Black or Blue ink; otherwise only 50% of
score is recorded.
2. Students caught cheating will automatically get a grade of 5.0 in this
course.
3. Do not round off intermediate values. Final answers should be given
in exactly 5 significant digits.
4. Box final answers. Should there be ambiguity on what your final
answer is, you stand to lose all the points in that item.
5. Late papers will receive a 1point penalty for every minute late.
6. Use of cell phones is prohibited.
7. Use only the right side of your bluebook. Use the left side for
scratch. The teacher will not check stuff written on the left side of
the bluebook.
8. No borrowing of calculators between students. In case two students
are caught sharing a calculator, teacher will keep said calculator for
the duration of the test.
9. Insert questionnaire in bluebook after the test. Bluebooks with no
questionnaires inserted will not be checked.
Highest possible score: 121/120 (101%)
Passing:
71/120 (60%)
I. Possible or Impossible
. If the descriptions provided could not possibly
occur within the rules governing probability distributions or mathematical
laws in general, mark the item Impossible. Otherwise, mark it Possible. (20
points  2 points each)
1. A random variable with pdf, f(x) = x for 0 < x <
√
2 (0 otherwise).
2. A random variable with cdf, F(x) = 1 for 5 < x < 10 (0 otherwise).
3. A random variable with pdf f(x) = e
x
for x
≤
0 (0 otherwise).
4. A random variable with cdf defined as follows:
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View Full Document5. A random variable with pdf defined as follows:
6. A gamma random variable, X, with
7. A normally distributed random variable with standard deviation of 0.
8. A uniformly distributed continuous random variable, X, with
9. Positive numbers a and b such that a < b and
Γ
(a) >
Γ
(b).
10.
A value for k such that P(X < k) = 0 for the lognormal random
variable X.
II. True or False
. If the statements provided are necessarily true, mark
the item True. Otherwise, mark it False. (11 points  1 point each)
1. The Central Limit Theorem guarantees that if we take enough
observations of a random variable X, the distribution of the variable
will approach the shape of the normal distribution.
2. The Central Limit Theorem applies only to continuous random
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