Abstract Algebra
1) Solve the equation
x 25 x +6=0the ring Z 12.
Sol: Given equation is
x 5 x +6=0.
2
In the ring of integers Z, which has no zero divisors,
2
x 5 x +6=0 ( x2 )( x3 ) =0 has two solutions2,3 Z .
But Z 12 ; for x=6, ( x2 )( x3 ) =( 4 )( 3 )
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‘v
am CHAP. 25 Mathematical Suﬁ-mu
Fxgm'eSAi-O on p. IO'IS shows an example. Since AOQ(O} -=
9*. giving the average on
cmhnamaximummm6=
-. ’ 11—- OLB?EE?LEESIETE253 6.:—‘_
ledhimminapembynampﬂngplmthu
m'amkufamwmmmnmbu
lmthappenainﬁuhlifmaumphﬁuiﬂnuwed
Chapter 5 Goodness of Fit Tests
5 GOODNESS OF
FIT TESTS
Objectives
After studying this chapter you should
be able to calculate expected frequencies for a variety of
probability models;
be able to use the 2 distribution to test if a set of observations
fit
To solve y = ax2 + b for x when y = 0, a = 1, and b = 2
S,(Y)Ss(=)S-(A)
Y=AX 2 +B _
S)(X)w+Se(B)
1s(SOLVE)
Prompts for input of a value for Y
Y?
0.
Current value of Y
0=
A?
1=
X?
c
B?
- 2 =f
X?
1s(SOLVE)
To exit SOLVE: A
X=
1.414213562
Solution screen
Imp
Math
3=
Math
Input an initial value for X (Here, input 1):
1=
Math
= 7 =
Math
= 13 =
Statistical Calculations (STAT)
To start a statistical calculation, perform the key operation N3(STAT)
to enter the STAT Mode and then use the screen that appears to sele
Statistics
Chapter Three: Testing Hypothesis
1
Introduction
Statistical inference is the science of drawing conclusions about a population based on information
contained in a sample. A particular type of inference is involved with the testing of hypothese
Indian Institute of Space Science and Technology
B.Tech Aerospace, Avionics & Physical Sciences
MA-311 PROBABILITY AND STATISTICS
Tutorial on Statistics
1. A certain component is critical to the operation of an electrical system and must be replaced immed
Statistics
Chapter Two: Estimation
Estimation: Suppose be a parameter of a population to be estimated. Now according to the
information on two types of situation may occur:
Case-I: The population parameter is totally unknown and on the basis of a sample d
Indian Institute of Space Science and Technology
Assignment
B.Tech 5th Semester
MA 311 - Probability and Statistics
1. Let X1 & X2 are independent random variables. Show that X1 X2 & X2 are never
independent.
2
n
n
1
n
2. Show that S 2 =
Xi 2
Xi .
n(n 1)
Statistics
Chapter One: Sampling Distribution
Denition.
1. The totality of the observations with which we are concerned is called a population.
2. The number of observations in the population is dened to be the size of the population.
3. A subset of a pop
FUNCTIONS
2
1) On what domain the functions f ( x )=x 2 xg ( x ) =x +6 are equal ?
2
Sol: Given functions is f ( x )=x 2 xg ( x ) =x +6 .
Now we find out the both functions are equal and domain.
We have f ( x )=g ( x )
2
x 2 x=x +6
2
x 2 x + x6=0
x2 x6
Linear Differential Equations
d2 y
dy
3 +2 y=0 .
2
dx
dx
1) Solve
2
Sol: Given equation is
d y
dy
3 +2 y=0
2
dx
dx
In Symbollic form can be written as
[
( D2 y3 Dy+ 2 y ) =0 D=
2
dy
d y
D 2= 2
dx
dx
]
( D23 D+ 2 ) y=0
( m23 m+ 2 )=0
Auxillary equationis
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