Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
3.1 DIFFERENTIATION RULES
d ( f ( x) g ( x)
dx
Find f and its first three derivatives
f ' ( x) g ( x)
d (a )
0
dx
d ( x n ) nx n1
dx
x
d (e ) e x
dx
d ( af ( x) a f ' ( x)
dx
d (a x )
Find f ' ( x) for:
a ln a
x
dx
3
a) f ( x) 4 x 2 x 7
2
2
b) f ( x ) x
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
11.8 POWER SERIES
(1)n ( x 1) n
n3
n 0
THEOREM
For the given power series
c
n 0
i)
ii)
iii)
n
( x a) n , there are only three possibilities:
The series converges only when x = a
The series converges for all x.
There is a positive number R such that the s
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Spring 2015
Solutions To Mathematics
Textbooks/Probability and Statistics for
Engineering and the Sciences (7th ed)
(ISBN10: 0495382175)/Chapter 3
1
Section 3.1  Random Variables
1.1
Z = the number of pumps providing both Diesel
and Gasoline.
Exercise 1
Let X b
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Spring 2015
Solutions To Mathematics
Textbooks/Probability and Statistics for
Engineering and the Sciences (7th ed)
(ISBN10: 0495382175)/Chapter 4
1
Section 4.1
1.1
P (2 < X < 3) =
3
1
dx
2 10
=
1
2
Exercise 1
cfw_
Given the density function f (x) =
0.5x 0 x 2
0
Project 2 Working
Hypothesis testing
1. (a) Appropriate ttest
The appropriate ttest for comparing the mean cell lengths of the diseased and the
healthy groups is the independent ttest or the sample ttest. The independent ttest
determines whether ther
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
11.3 THE INTEGRAL TEST
Suppose f is a continuous, positive, decreasing function on [1, ) and let
a n f (n) . Then the series
a
n 1
n
Use the Integral test to determine if the series is divergent or convergent.
n
n 0
2
ln( n)
n
n 1
1
3n 2
is convergent if