DUE: Thursday, February 13 in class or handed in to my office before 5:00 pm
Let Y 1 , Y 2 , ., Y n be a random sample from a Gamma distribution with = 2 and unknown
parameter = > 0 , i.e. (2, = ) , with pdf f(y : ) = 2 y e-
Final Review Problems STAT 3509
To Review the earlier part of the course go back over previous review & practice problems, notes,
assignments, tutorials, tests, etc. ‘
Text 7.1.1 Show that the mean E of a random sample of size n f
STAT 3509 MATHEMATICAL STATISTICS
Introduction to Mathematical Statistics, 6th or 7th ed, by R.V. Hogg, J.W. McKean, A.J.
Mathematical Statistics, by Freund, J.M.
Set up and Differentiation Practice
ln f(x : )
ln f(x : )
for the unknown parameter
. Remember that what you want to do is get ln f(x : ) in a form such that as many as possible of the
terms do not involve the parameter that you are intereste
E LX) -
1.2, 7 (<*)
U 2 '
If X 1 , X 2 , ., X n constitute a random sample from the population with pdf
e-(x - )
Show that X is a biased estimator of . What is the bias?
What estimator based on X would be an unbiased est
Practice Problems 3
If X 1 , X 2 , . , X n constitute a random sample from a Beta distribution with = 1,
Use the Method of Moments to find an estimator for the parameter .
Use the Method of Maximum Likelihood to find an estimator for .
Practice Using Rules of Logarithms and Differentiation of ln Functions
Simplify the following expressions
4. ln 4
3. ln [ x e ]
x + 1 )3 (2x - 3 )5
2 - x/
3 x e
Review Problems Part 1 : Final Exam
For all hypothesis test and confidence interval questions state any assumptions needed for your
tests and C.I.s to be valid.
The amount of shaft wear(.0001 in.) after a fixed mileage was determined for each of n = 8
Some More Practice Problems
Remember Test problems:
9.81, 9.83, 9.85(a),(b), 9.97 ADD 9.82
In measuring the reaction time to a certain stimulus, it is known that the standard deviation is 0.05 sec.
How large a sample of measurements must be t