Problems with solutions -MS Exam: Option I
Probability and Statistics- Fall 2007
[1]
Math 310 -MS Exam, Fall 2007
If A is a real symmetric matrix then show that its range (column space) R(A)
and null space N (A) have only the null vector in common, i.e.,
The written Masters Examination
Option Statistics and Probability
SPRING 2009
Full points may be obtained for correct answers to 8 questions. Each numbered question
(which may have several parts) is worth the same number of points. All answers will be
gra
The written Masters Examination
Option Statistics and Probability
FALL 2009
Full points may be obtained for correct answers to 8 questions. Each numbered question
(which may have several parts) is worth the same number of points. All answers will be
grade
Masters Written Examination
Option: Statistics and Probability
Fall 2013
Full points may be obtained for correct answers to eight questions. Each numbered
question (which may have several parts) is worth the same number of points. All answers
will be grad
The written Masters Examination
Option Statistics and Probability
SPRING 2010
Full points may be obtained for correct answers to 8 questions. Each
numbered question (which may have several parts) is worth the same number
of points. All answers will be gra
MS exam problems Fall 2012
(From: Ryan Martin)
1. (Stat 401) Consider the following game with a box that contains ten ballstwo
red, three blue, and ve green. A player selects two balls from the box at random,
without replacement. The player wins $5 for ea
Masters Examination Solutions
Option Statistics and Probability
Spring 2011
1. (STAT 401)
Suppose that X exp() with pdf f (x; ) = ex for x > 0.
(i) Show that P (X > x) = ex for x > 0, and prove that E(X) =
0
P (X > x)dx.
(ii) Suppose Y exp(), and X and Y
The written Masters Examination
Option Probability and Statistics
Fall 2008
Full points may be obtained for correct answers to 8 questions. Each numbered question
(which may have several parts) is worth the same number of points. All answers will be
grade
The written Masters Examination
Option Statistics and Probability
Fall 2010
Full points may be obtained for correct answers to 8 questions. Each
numbered question (which may have several parts) is worth the same number
of points. All answers will be grade
MS exam problems Spring 2012
(From: Ryan Martin)
1. (Stat 401) Suppose you have a bag that contains three six-sided dice: two of the
dice are fair (all six sides have 1/6 probability), but the third die is irregular, having
probabilities given in the foll
Masters Examination Solutions
Option Statistics and Probability
Fall 2011
1. (STAT 401)
Suppose that X, Y and Z are i.i.d. Uniform(0,1). Let t > 0 be a xed constant.
(i) Compute P ( X t).
Y
(ii) Compute P (XY t).
(iii) Compute P ( XY t). (Hint: P ( XY t)
Masters Written Examination
Option: Statistics and Probability
Spring 2013
Full points may be obtained for correct answers to eight questions. Each numbered
question (which may have several parts) is worth the same number of points. All answers
will be gr