HUDM 4122: Probability and Statistical Inference
Practice Midterm
1
MIDTERM
SHOW YOUR WORK
Please round all numbers to FOUR decimal places.
1.
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D,
and E are female. The personne

Statistical Methods used in Statistical Inference
Descriptive Statistics
Used to summarize and describe important characteristics of a set measurement's usually in the form of:
graphs such as: bar chart, pie chart, histogram, polygon, etc.
numerical mea

HUDM 4125 - Statistical Inference
HW 1 - Solutions
1
Problem 2
(a) Show that P () = 0.
1. Note that = and = .
2. Let A1 = , let Ai = for i > 1.
!
[
X
3. P
Ai =
P (Ai ) by Axion 3.
i=1
i=1
4. P () = P () +
0=
X
X
P ()
i=2
P ()
i=2
5. Because P ()>0,
X
P ()

HUDM 4125 - Statistical Inference
Homework 5
=
Problem 1. E()
n
1 X
1
E[
Xi ] = n =
n
n
i=1
=0
Bias()
v
r
r
u
n
p
u1 X
1
t
SE() = V ar() =
n =
V ar(Xi ) =
2
2
n
n
n
i=1
= Bias()2 + V ar()
=0+ =
M SE()
n
n
Problem 2.
( 1
So, Fy (y) =
0
,0 x
,x >

HUDM 4125 - Statistical Inference
Problem 1. Let Z =
var(X) = 2 , then
X
. Chebyshevs inequality states that if mean of X is and
2
.
t2
P (|X | t)
Set t = k to get
P (|X | k)
2
.
(k)2
Then,
X
1
P
k 2.
k
By definition of Z,
P (|Z| k)
1
.
k2
Proble

HUDM 4122: Probability and Statistical Inference
1
MIDTERM
SHOW YOUR WORK
1.
Five applicants apply for two jobs. Applicants A and B are male; applicants C, D,
and E are female. The personnel officer selects two applicants at random to fill the
two jobs.
a