CHAPTER7 Estimation
Point Estimation : Definition : Point estimation is a choice of statistics, i.e. a single number calculated from sample data for which we have some expectation, or assurance that it is reasonably close to the parameter it is supposed
Lecture No: 10 Sampling with replacement : If we choose randomly with replacement a sample of n objects from N objects of which r are favorable and X= number of favorable objects in the sample chosen, then X has binomial distribution with parameters n and
Limits of Point estimation
In point estimation, statistic is used to estimate population parameter. Statistic is a function on random sample. From a particular sample, value of that statistic is used to estimate the parameter. This is not the actual value
What is Simulation?
Dr. Bimal Kumar Mishra, Maths Group, BITS, Pilani
Simulation Is .
Very broad term, set of problems/approaches Generally, imitation of a system via computer Involves a model validity? Dont even aspire to analytic solution
Dont get exa
Mathematical Expectations
Dr.Bimal Kumar Mishra, Maths Group, BITS, Pilanii
Expected value
Let (X , Y )be two dimensional random variable with joint density fXY. Let H(X,Y) be a random variable. The expected value of H(X,Y) , denoted by E[H(X,Y) ] is give
What is there in the handout? What
Maxwells equations and electromagnet ic waves Basic equations of electromagnetism, induced magnetic fields & the displacement current, Traveling waves & Maxwells equations, (also in differential forms). Energy transport
Lecture # 23 Conditional Densities: The conditional density for X given Y=y denoted by fXy,
P[X = x and Y = y] P[X = x and Y = y] = P[Y = y] f XY ( x , y) = f Y ( y)
Def: Let (X,Y) be a two dimensional random variable with joint density fXY and marginal
Chapter # 5 Joint Distributions Single Random Variables:
Discrete
Continuous
Univariate
Two Dimensional Random variables
Discrete
Continuous
Bivariate
Discrete Joint Density: Let X and Y be discrete r.v, the ordered pair (X,Y) is called a two dimensional
Lecture # 15
Exponential Distribution
In Gamma Dist. Put =1, we get f(x)= exp(x / )/ ; x > 0, > 0 =0 ; e.w .
f(x)
=1, =1
The distribution arises in practice in conjunction with the study of Poisson processes, where we have discrete events are being obs
Lecture # 15
Exponential Distribution
In Gamma Dist. Put =1, we get f(x)= exp(x / )/ ; x > 0, > 0 =0 ; e.w .
f(x)
=1, =1
The distribution arises in practice in conjunction with the study of Poisson processes, where we have discrete events are being obs
Chapter # 2 Axioms of Probability: Let S denote a sample space for an experiment, then P[S]=1 P[A] 0 for every event A Let A1,A2,A3, be a finite or an infinite collection of mutually exclusive events, then P[A1A2 A3.]=P[A1]+P[A2]+p[A3]+.
The first two axi
Lecture # 22
Independent random variables
Ex Store A and B, which belong to the same owner, are located in 2 different towns. If the density function of the weekly profit of each store, in thousands of rupees, is given by
x / 4 if 1 < x < 3 f ( x) = othe
Computer Programming TA C162
Algorithms and Problem Solving
What is an Algorithm? Algorithm Properties Representation of Algorithm i.e. Flow Chart Examples
Second Semester 20082009
1
Computer Programming TA C162
Solving Problems using a Computer
Methodol
Chapter 7 Lecture # 29 Estimation
To estimate numerical value of a population parameter using a sample of some size n. We must device an appropriate statistic (on random sample of size n) so that we only need to consider its value on the observed sample.
Chapter 7 Lecture # 29 Estimation
To estimate numerical value of a population parameter using a sample of some size n. We must device an appropriate statistic (on random sample of size n) so that we only need to consider its value on the observed sample.
CHAPTER6 Lecture # 27 & 28

DESCRIPTIVE STATISTICS
Statistics
In Statistics, we want to study properties of a (large) group of objects, generally termed as population. Methods of statistics study small subsets of population. This is called sample. The s
CHAPTER11 SIMPLEREGRESSIONANDCORRELATION
1
Inthischapter,welearntoestimatethecurveofregression ofYonXwhentheregressionisconsideredtobelinear. LinearcurveofregressionofYonX
Y  x = 0 + 1 x
Where 0and 1denoterealnumbers.
11.1MODELANDPARAMETERESTIMATION From
CHAPTER9 INFERENCESON PROPORTIONS
Thischapterwill dealwithinferencesonproportionsand comparisonsoftwoproportions. We will see how to employ the standard normal distribution to construct confidence intervals on p and testhypothesesconcerningitsvalueforlarg
Chapter 9 Inferences on Proportions
This chapter will deal with inferences on proportionsandhypothesistestsonthem. We will see how to employ the standard normaldistributiontoconstructconfidence intervals on p and test hypotheses concerningitsvalueforlarge
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI SECOND SEMESTER 20072008 MATH C192 : MATHEMATICS II COMPREHENSIVE EXAMINATION (CLOSED BOOK) Date: 542008 Max Time : 150 Min Max. Marks 90 Note: Answer Part A and Part B in separate answer sheet. Write
Matrices of linear transformation & eigen values eigen vectors
Rajiv Kumar Math II
1
Definition:Naturalmatrixofa lineartransformationT:VnVm
Rajiv Kumar Math II
2
Example:
Let T: V3 V3 be a linear map,
definedby
T ( x1, x2 , x3 )
= ( x1 x2 + x3 , x2 x1, x
x Q. If u ( x, y ) = 2 , find a 2 x +y harmonic conjugate v of u. Soln : Observe the following :
1 (i ) If f ( z ) = , then u = Re f ( z ). z (ii ) f ( z ) is analytic in a domain D = C  cfw_(0, 0). y (iii) Im f(z) = v = 2 . 2 x +y Conclude that v is a H
System of Linear Equations
Rajiv Kumar Math II
Determinant and their properties
(i) det (AT) = det (A) (ii) det (C)= det (A) if C is determinant of matrix where two rows of A are interchanged. (iii) If two rows or two columns of A are identical then det
Chapter 7: Evaluation of Improper Integrals Advice 1: Page No. 257: Q. Nos.: 1  5
(1) Let f(x) is continuous for all x 0, then
0
f ( x)dx = lim
R
0
R
f ( x) dx
provided the limit on RHS exists.
( 2) Let f(x) is continuous for all x.
then
= lim
 0
f (
ANTIDERIVATIVES Let f(z) be continuous function in a domain D. If there exists a function F(z) such that
F ( z ) = f ( z ) for all z in D,
then F(z) is called an antiderivative of f(z) in D.
Remark1: An antiderivative of a given function f is an analytic
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI II Semester 20052006, Math C 192 Mathematics II Assignment sheet for Quiz IV Q.1 Prove the inequality  z1 z2    z1 z2  Q.2 Using the fact Prove equation  z1 z2  for z1 & z2 any complex numbers.
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI II Semester 20052006, Math C 192 Mathematics II Assignment sheet for Quiz III 13 Feb 2006
Q.1 Find a linear transformation T : V3V3 such that ker (T) = cfw_ (x,y,z) : 3xy+z=0 & xy+z=0, justify your answer
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI II Semester 20052006, Math C 192 Mathematics II Assignment sheet for Quiz II Page 93 Q.1(a), (c) Q 2 (b) Page 94 Q.3 (a) , (d) Q.4 (e) Page 104 Q.1 (a) , (d) Q.2 (d), (f)
U = cfw_( x , x , x ) / x x + x
1 2
LINEAR ALGEBRA with Applications
BERNARD KOLMAN DAVID R. HILL
MATRIX : An m x n matrix A is rectangular array of mn real numbers arranged in m horizontal rows and n vertical columns. Elementary Row Operations : 1. Ri Rj 2. Ri t Ri 3. Ri Ri + t Rj , t is
Eigen Values & Eigen Vectors
Let A be n x n matrix. is eigen value of A if there exists a nonzero vector n x R such that Ax = x x is called an eigen vector of A associated with
Eigen value / proper value / characteristic value / latent value eigen vector