Exercise 1-5
Given: Three common building insulations.
Required: Thermal resistance in terms of "R" value.
Assumptions: 1. One dimensional conduction.
(i) R value of 10 cm thick berglass? Table 1.1 gi
The Exponential Distribution (section 4.2)
The exponential distribution is often used to
model failure times OR waiting times OR
interarrival times
Probability Density Function
f(x) = ex , x 0, > 0
Cu
The Weibull Distribution (section 4.4)
The Weibull distribution is often used to
model the time until failure of many
different physical systems.
It has the following probability density
function:
f(x
Chapter 5 The Normal Distribution
In this chapter we discuss the most
important special type of continuous
distribution:
The Gaussian distribution
or, as it is more commonly referred to,
The normal di
Normal Random Variables
1.
2.
3.
There is a probability of about 68%
that a normal random variable takes
on values within 1 standard deviation
of
There is a probability of about 95%
that a normal ran
Case (II): Non-pooled Two Sample t-test
The underlying population standard
deviations are unknown, but are NOT
assumed to be equal
That is, x y
Substitute s2x for 2x and s2y for 2y
This leads to the f
(III) Dependent Samples: Inference
About the Difference Between Two
Population Means Paired t-Test
(section 9.2)
We start off with a 2-sample problem:
Xi = sample data from population1
Yj = sample dat
Type I and II Errors
Suppose we are performing a one-sample
t-test of
H0: = 0
HA: 0
There are 2 possible errors that can be
made:
Our
Decision
Do not
reject H0
Reject H0
True Situation
H0 is true
H0 i
SECTION 2.1 (PAGE 98)
R. A. ADAMS: CALCULUS
CHAPTER 2.
Section 2.1 (page 98)
DIFFERENTIATION
7. Slope of y =
x + 1 at x = 3 is
Tangent Lines and Their Slopes
1. Slope of y = 3x - 1 at (1, 2) is
m = l
INSTRUCTOR'S SOLUTIONS MANUAL
SECTION 1.1 (PAGE 61)
CHAPTER 1.
LIMITS AND CONTINUITY
7.
Section 1.1 Examples of Velocity, Growth Rate, and Area (page 61) 1. 2.
(t + h)2 - t 2 x = m/s. t h
At t = 1 the
The Gamma Distribution (section 4.3)
As we saw in the last section, an
exponential random variable describes
the length of time or distance until the
first count is obtained in a Poisson
process
A gen
Combinations and Functions of Random
Variables (section 2.6)
1. Linear Functions
If X is a random variable and a, b are
constants, then
Y=aX+b
is also a random variable, and
(i) E[Y] = a E[X] + b
(ii)
Chapter 3 Special Types of Discrete
Distributions
The Binomial Distribution (section 3.1)
Bernoulli Random Variables
Let X be a random variable that can take
on only two possible values:
X = 1 if a su
Exercise 2-3
Given: A slab made up of n pairs of square bars of conductivities RA and k3, as shown.
Required: (i) Effective conductivity across the width.
(ii) Effective conductivity through the thick
Exercise 2-15
Given: Milk at 5C owing inside a stainless steel tube insulated with a 5 cm thick
layer of cork.
Required: Calculate the rate of heat gain per meter length of tube.
Assumptions: 1. One-d
Fins
Ac is the cross sectional area
P is the perimeter
L Length
nf = effiency
B = (hcP/KAc)^1/2
X = BL
nf= TANHX/X
Q = h(PL)(Tb-Te)
Q = (hcP/B)(Tb-Te)TANH(BL)
Q = KaB(Tb-Te)TANH(BL)
Q = INT(0,L) (T-Te
Chapter 1
Q = qa
Q = Delta T / Sum R
R = La / Ka
If area can be found
R = La / KaA
q = (Ti-T1)/(La/Ka) = (T2-To)/(Lb/Kb)
Q = (To - Ti) / (L/K Area)
Since its a cube not a wall
Small Grary body in nea
(II) Jointly Distributed Continuous
Random Variables
For two continuous random variables
X and Y, the joint probability density
function is given by f (x, y),
where
f (x, y) 0 for all x and y and
f (
Jointly Distributed Random Variables
(section 2.5)
So far we have studied probability
distributions for a single random variable
However, many experiments are
conducted where two random variables
are
Two Continuous Random Variables
The conditional distribution of X given a
fixed value of Y is given by:
f ( x, y )
fX|Y = y (x) =
fY ( y)
The conditional distribution of Y given a
fixed value of X is
The Multinomial Distribution (sect. 3.5)
Suppose you have a situation where:
1.
You have a fixed number of trials
trials)
(n-
2. The trial are independent
However, instead of having only two
possible
Note
When do you use the binomial
distribution and when do you use the
hypergeometric distribution?
You must have a situation where there
are only two possible outcomes on each
trial: success or failu
(II) Negative Binomial Distribution
(section 3.2)
This distribution is used when trying to
determine how many trials are needed in
order to obtain r-successes
Let
X = number of trials needed to obtain
INSTRUCTORS SOLUTIONS MANUAL
APPENDIX I. (PAGE A-10)
APPENDICES
15.
Appendix I. Complex Numbers (page A-10) 1. z = 5 + 2i ,
Re(z ) = 5, z = 5 + 2i z = 6 z = 4i z = i Fig. .1 x Im(z ) = 2 y z -plane
16
Chapter 1 Stress
Review of Statics (1.1-1.2)
External loads
Surface force (N/m2)
concentrated force (N)
linear distributed load (N/m) (can be replaced by a resultant force)
Body force (can be repres
MME 2202a Mechanics of Materials
Prof. L.Y. Jiang
Office:
Rm 3076 SEB
E-mail:
[email protected]
Prerequisites:
ES1022a/b/y, AM 1413 or
written permission from your Dean
Teaching Assistants:
Assignmen
Chapter 2 STRAIN
(2.1, 2.2)
Two types of strain:
Normal strain, =
Change in length resulting from applying a normal stress
unstressed length
Shear strain, = Angle of twist resulting from an applied sh