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Part II
Probability, Random Variables, and Sampling Distributions
Chapter 5: Probability and Random variable
Introduction
In inferential statistics, we use the sample to draw conclusion about population, but we can never be
certain our conclusions are cor
Answers to selected problems of Chapter 2
2.8
2.24
a) The scores of students (out of 100 points) on a very easy exam in which most score perfectly or nearly so, but a few score
very poorly skewed to the left because of the few who score poorly
b) The week
Math 2300 - Fall 2013
Class Test 01
Name
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) The table below shows the average income by age group for the residents of one town in the year 1)
1998.
2300 Final Review
November 30, 2014
Chapter 1
The Nature of Statistics
1.1
Statistics Basics
Descriptive Statistics consist of methods of organizing and summarizing data. Note: Descriptive statistics only summarize and organize the
data set at hand and d
Practice test1
Name_
This are just some practice questions. Their purpose is for you to get accustomed to
the format of the real test. The questions onthe actual test will test the same concepts
, but , will NOT be the same as on these practice questions.
Review 03
Chapter 7,8 and 9
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) The test scores of 5 students are under consideration. The following is the dotplot for the sampling
distribution of the
Exam I Review
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) The table below shows the average income by age group for the residents of one town in the year
Math 2300- Fall 2013
Review 01
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) The table below shows the number of new AIDS cases in the U.S. in each of the years 1
SURFACES and SLICING
Just as having a good understanding of curves in the plane is essential to interpreting the concepts of single
variable calculus, so a good understanding of surfaces in
3-space is needed when developing the fundamental
concepts of mul
Gradient, Chain Rule, and Directional Derivatives
What's going to replace the derivative
f (x) of a function y = f (x) of one variable when f is a real-valued function
of two or more variables? Since slope now depends on direction, not just sign, we can e
DOT and CROSS PRODUCTS
So far we've added vectors, subtracted them, and multiplied by a scalar, but now it's time to 'multiply' two
vectors. There are two different products, one producing a scalar, the other a vector. Both, however, have important
applic
Higher Order Derivatives, Taylor Approximations
Second order partial derivatives can be defined just as in the one variable case. We simply differentiate partially twice to
obtain
fjj = (fxj )xj =
2 f
(fxj ) =
,
xj
x2
j
fkk = (fxk )xk =
2 f
(fxk ) = 2
,
x
3D-COORDINATE SYSTEMS
When there's symmetry present, it's often helpful to use coordinate systems that rely on this symmetry, say when studying
a torus or motion on a spiral staircase. In three dimensions two particularly useful ones are Cylindrical Polar
CONSTRAINED OPTIMIZATION
By now you're used to finding maxima and minima of both single- and multi-variable functions. But what if a restriction is
placed on the variables? Such so-called Constrained Optimization Problems come up frequently in application
LINES and PLANES in 3-SPACE
2-space (you probably learned the slope-intercept and pointslope formulas among others, for example). Now we do the same for lines and planes in 3 -space. Here vectors will be
There are many ways of expressing the equations of
VECTOR CALCULUS: setting the scene
So far differential and integral calculus have been developed for scalar-valued functions
y = f (x),
z = f (x, y),
w = f (x, y, z)
of one, two or three variables. In practice, however, many functions we encounter are vec
EXTREMA of REAL-VALUED FUNCTIONS
Optimization of functions is just as important for functions of several variables as it was in one variable. Let's
first look at things graphically. The interactive surface to the right below is one we've met before. It's
PATHS, CURVES, and DIFFERENTIATION
Now we turn from surfaces to paths and curves in
3-space, but from a vector point of view. Let
r(t) = U R R3 = x(t) i + y(t) j + z(t) k
x(t), y(t), and z(t) which we assume have continuous derivatives. It is
r(t) as a po