MATH 4581
Statistics and Stochastic Processes
February 18, 2014
Test 1 practice problems
Name:
Practice problems are slightly harder, and the list is longer than the actual exam. The exam will be
worth up to 35% of the course letter grade, so make sure to

yqm ayxx Synnj'ZDNa
QM), E KLVICU Angwwj
Q) A: (a j /A: L905 = 7; 52,9" x/L: Li/J
8(W): E(T)/lj\' krw E(/Z):\5(W):l7
J .,_._.-
v 9!:
b) rkt DVDO U A)": : 15 1:20
I - asa .1" 7 i561;
wis"; mHl: * m IS
05 Ber f Jf,. fa M i 8 )0 16 m
xv af 4>m=M(3 4 m

., m6
W
Spring 2016 Math 4581 Test 2 Name:_._&;s_
Show your work!
1. A store gets 50 customers per hour on average. If this is a Poisson process (Give your answers as a
formula and to three decimal places):
a) (6 pts) nd the probability that they will get

Name (at IA 5mm 125
Math 4581 Final Exam Spring 2015
1. A study is looking to see which method works best to heal a leg injury. They break patients into four
groups With the following results (in days until recovery):
Physical Therapy and drug A (group

um 445; 5W7 mm
j: m. LL? a my; D r: 3 30M ~ 9"
I (if cfw_wa-A
/
n , I m x M U M" 1 I 6: L
b) j (w) :9 7714.; j A a 2/2., cfw_Lia ) 2 (2:;wa 1' Mag: IL) 4mm
41: cfw_D 5 t : iqufB
a E cfw_:3 7 I: if 3 Z/" I Jpn ~ ,LMQZA)
Liv-7L) y3~f<33u3)/Iwr3

rm
Jars
A 9
Spring 2016 Math 4581 Quiz 3 Name: ;
Show your work!
1. For an M/ M / 1 system, where 12 jobs arrive each minute on average and it takes 4 seconds to nish each:
a) (4 pts) nd E(N), E(Nq), EXT), and E(W).
, .317;
>\=IL A: i? 9 f0 33 /5
I / i

Spring 2016 Math 4581 Quiz 1 Name: W
1 k/2
1. The moment generating function for the X2 distribution with k degrees of freedom is (1 2t)
X is a X2 distribution with 10 degrees of freedom and Y is a X2 distribution with 20 degrees of freedom. If
X and Y

Spring 2016 Math 4581
Quiz 2 Answers
.4 .6 0 0
0 .4 .6 0
1. Given the transition matrix with states 1,2,3,4: P =
,
0 0 .4 .6
.1 0 .4 .5
a) (5 pts) The vector w = (1/13, 1/13, x, y) is the fixed vector. Find x and y (show your work).
Answer:
wP .4
x=1
1

MATH 4581
Name:
Quiz 1
January 23, 2014
2
1. If X is a random variable with probability density function f (x) = 2xex ,
probability density function, g(y) = ey , y > 0.
x > 0, show that Y = X 2 has
2. USA Today reported that 21% of loans granted by credit

Spring 2016 Math 4581
Quiz 3 Review
1. For an M/M/1 system, where 6 jobs arrive each hour on average and it takes 8 minutes to finish each:
a) find E(N), E(Nq ), E(T), and E(W).
b) give the density function for T and use it to find P (T < 20 minutes).
c)

Spring 2016 Math 4581
Quiz 1 Review Answers
1. Find the moment generating function for each of the following:
5
for k = 1, 2, 3, 4
a) P (X = k) =
4k(k + 1)
Answer: P(X=1)=5/8, P(X=2)=5/24, P(X=3)=5/48, P(X=1)=1/16
MX (t) =
5 1t
5
5
1
e + e2t + e3t + e4t

Spring 2016 Math 4581
Quiz 1 Review
1. Find the moment generating function for each of the following:
5
for k = 1, 2, 3, 4
a) P (X = k) =
4k(k + 1)
b) P (X = k) = (k + 1)(1 p)k p2 for k = 0, 1, 2, . . . Use:
X
kxk1 =
k=1
c) fY (y) =
1
if |x| < 1.
(1 x)2
1

Spring 2016 Math 4581
Quiz 2 Review
.5 .5 0 0
.1 .5 .3 .1
1. Given the transition matrix P =
,
0 .2 .6 .2
0 0 .3 .7
a) set up the equations to find the fixed vector.
b) show that w = (3/73, 15/73, 30/73, 25/73) is the fixed vector.
c) find the mean ret

Spring 2016 Math 4581
Test 2 Review
1. For M/M/2/3 where 2 message arrive each second on average and it takes 1 second to process each:
a) solve for the steady state probabilities p0 , p1 , p2 , and p3 .
b) find E(N) and E(T).
2. For the M/M/1 system, whe

Spring 2016 Math 4581
1. Given below are some points:
x
15
18
19
22
y
52
51
42
48
Test 1 Review
22
45
25
47
26
41
30
38
a) Test at the 5% level to see if the slope of the regression line is 0. Give the p-value and decide if you accept
or reject the null h

Spring 2016 Math 4581
Final Review
Note: Problems 1-8 and 16-17 are from the Spring 2015 Final.
1. A study is looking to see which method works best to heal a leg injury. They break patients into four
groups with the following results (in days until recov

MATH 4581
Statistics and Stochastic Processes
February 15, 2014
Test 1 practice problems
Name:
Practice problems are slightly harder, and the list is longer than the actual exam. The exam will be
worth up to 35% of the course letter grade, so make sure to