Statistics 4150 Cheat Sheet
Random Probability Facts
V ar(X)
Chebyshev inequality: P (|X | t)
t2
P (|X | k) 12
k
P (|X | k) 1 12
k
There are two different formulations of the geometric, (1) corresponds to the the probability that trial
x is the first suc
Midterm
Stat W4150
Professor Protter
October 22, 2015
Please do all the Problems. Tables are provided. Calculators without internet access
are allowed, but this exam is closed book, closed notes, closed files. No cell phones
are allowed, or any type of me
2 Probability
.ymbol
id the bottom
state this more
.110 and 2 double
j
electing r objects \
,mbinations. A "
containing the
that are left. The
time is
T‘
._.
a
E
d
r:
_.
m
8
z
,D
H
5"
o
_
Jhat his mother
E
o
s".
Ewercises
51
Using the multipli
38
Figure 2.4: Events of the sample space 5'.
Exercises '
2. 1 List the elements of each of the following sample
spaces:
(a) the set of integers between 1 and 50 divisible by 8;
(b) the set .5'={3: | mun—5:0};
(c) the set of outcomes when a coin is tossed
282 Chapter 9 One— and Two-Sample Estimation Problems ‘3
Thus, the 99% conﬁdence bounds are 0.9781 and 1.0331.
(b) The 99% prediction interval for a future observation is given by
e a: mow/1 + 1/71 = 1.0056 i(3.355)(0.0246)\/1+ 1/9,
with the bounds being
150
Chapter 5 Some Discrete Probability Distributions
Example 5.7 :|The complexity of arrivals and departures of planes at an airport is such that
computer simulation is often used to model the “ideal” conditions. For a certain
airport with three runway
230 - Chapter 8 Fundamental Sampling Distributions and Data Descriptions
Theorem 8.1: If 8'2 is the variance of a random sample of size n, we may write
1 ” 1 n _
2: X _ 2— X2_ 2 2
S —-n_1i§=1( , X) n_1z§:1( ,_ 2XX +X)
= 11[§:XE—T~2X§:Xi+nX'2].
n.—
222
Therefore,
Chapter 7 Functions of Random Variables (Optional)
Mye) z (1— arm/2a — aria/2 . - - (1 “ mafia/2 = ('1 — 2t)‘(“1+"2+'”+”")/2,
(
which we recognize as the moment—generating function of a chi—squared distribution
with 'v 2 121 + 112 + - - - +
334
Chapter 10 One— and Two-Sample Tests of Hypotheses
' ﬁxed oz approach that is climaxed with either a “reject H0” or a “donot reject H0”
conclusion and the P—value approach. In the latter, no ﬁxed a is determined and
conclusions are drawn on the basis
398
Exercises
11.1 A study was conducted at Virginia Tech to de~
termine if certain static arm—strength measures have
an inﬂuence on the “dynamic lift” characteristics of an
individual. Twenty—ﬁve individuals were subjected to
strength tests and then were
Exercises
—1
91
0.5
O 1 2
Figure 3.6: Continuous cumulative distribution function.
Thus,
1%) =
0, y<§b,
5 1 2
ﬁ—Zﬁ
1, y22b.
To determine the probability that the Winning bid is less than the preliminary bid
estimate b, we have
assify
Erercz'ses
185
Example 6.13: The average grade for an exam is 74, and the standard deviation is 7. If 12% of
Solution :
Figure 6.20: Area for Example 6.13.
the class is given As, and the grades are curved to follow a normal distribution,
what is the low
Emercises
Exercises
4.1 The probability distribution of X, the number of
imperfections per 10 meters of a synthetic fabric in con—
tinuous rolls of uniform width, is given in Exercise 3.13
on page 92 as
x 0 1‘ 2 3 4
f a: 0.41 0.37 0.16 0.05 0.01
Find the
SIEO%W4150%Probability%&%Statistics%2/1/2016%
Class%Summary%Notes%Chapter%3%
Copyright%Irene%Hueter%
%
SIEO%W4150%Probability%and%Statistics%
%
3. Random Variables and Probability Distributions%
Commonly
used
and
famous
distributions
will
be
introduced in
SIEO%W4150%Probability%&%Statistics%2/24/2016%
Class%Summary%Notes%Chapter%6%
Copyright%Irene%Hueter%
%
SIEO%W4150%Probability%and%Statistics%
%
6. Some Continuous Probability Distributions
Examples of popular continuous distributions that are
frequently
SIEO%W4150%Probability%&%Statistics%2/22/2016%
Class%Summary%Notes%Chapter%5%
Copyright%Irene%Hueter%
%
SIEO%W4150%Probability%and%Statistics%
%
5. Some Discrete Probability Distributions
Different statistical experiments can lead to the same
type of beha
STAT W4150 - INTRO PROBABILITY & STATISTICS
Course Logistics
Instructor:
IRENE HUETER
Email: irene.hueter@columbia.edu
ih2169@columbia.edu
Office: Room 901 SSW
(School of Social Work Building, 122nd St and Amsterdam)
Note: Room is in locked