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) f
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
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
September 11
Sometimes it is important to look at the
probability of an event occurring when another
event has already occurred.
For any two events, A and B, with P(B) > 0 , the
conditional probabilit
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
LAST WEEK (August 30)
Prediction on a statistic Experiment Outcomes
Simple or Compound Event A set
Use of set theory Complement, Union and Intersection
Venn diagrams
Lectures of M. Rahman
1
TODAY
Introduction to Probability and Statistics for Scientists and Engineers
STAT 355

Fall 2013
The Exponential Distribution
A continuous random Variable X, is said to have an
Exponential Distribution with parameter (>0) , if
the pdf of X is given by
f(x,) = exp(x) for x 0 and zero otherwise.
T
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
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
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 co