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) correspon
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, clos
2 Probability
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id the bottom
state this more
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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: |
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 =
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 “ide
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(
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
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
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 ind
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 prelimin
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
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