Descriptive Statistics
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
Some important terminology
Methods of data representation: frequency tables,
graphs, pie-charts, stem-leaf diagrams, scatter-plots
Data mean, median, mode, quantiles
Chebyshevs i

CL 202: Introduction to Data Analysis
Tutorial 5, 2015
Note:
All the problems are from the book titled Introduction to Probability
and Statistics for Engineers and Scientists" by Sheldon M. Ross, 4th
edition, Elsevier.
Use your non-programmable calculator

Indian Institute of Technology, Bombay
CL202: Introduction to Data Analysis
Chemical Engineering
Tutorial 1, 2015
Note: (i) All the problems are from the book titled Introduction to Probability and Statistics for
Engineers and Scientists" by Sheldon M. Ro

Indian Institute of Technology, Bombay
CL202: Introduction to Data Analysis
Chemical Engineering
Tutorial 4, 2015
Note: (i) All the problems are from the book titled Introduction to Probability and Statistics for
Engineers and Scientists" by Sheldon M. Ro

Tut? 3
4. The distribution lnction of the random variable X is given
0 x<0
x
05x<l
2
2
FOE): g 15:cfw_2
ll
25x<3
12
1 35:
(a) Plot this distribution function.
(b) What is Pcfw_X :> %9
(c) What is Pcfw_2 <: X 5 4?
(d) What is Pcfw_X <: 3?
(e) What is Pcf

Tut5
26. Suppose that two teams play a series of games that end when one of them has won
1' games. Suppose that each game played is, independently, won by team A with
probability p. Find the expected number of games that are played when i = 2.
Also show t

13. The joint density ofX and Y is TUt 4
2 U-ex<:_y,D-=:_y<1
ay):
0 otherwise
(a) Compute the density of X .
(b) Compute the density of 1.
(c) AreX and Y independent?
14. If the joint density function of X and Y factors into one part depending only
on x a

1. A box contains three marbles one red, one green, and one blue. Consider an
experiment that consists of taking one marble From the box, then replacing it in
the box and drawing a second marble From the box. Describe the sample space.
Repeat for the case

m2
1. A box contains three marbles one red, one green, and one blue. Consider an
experiment that consists of taking one marble From the box, then replacing it in
the box and drawing a second marble From the box. Describe the sample space.
Repeat for the c

TM? 511
1. An election will be held next week and, by polling a sample of the voting
population, we are trying to predict whether the Republican or Democratic
candidate will prevail. Which of the following methods of selection is likely to
yield a represe

45. A product is classied according to the number of defects it contains and the I
Factory that produces it. Let X1 and X2 be the random variables that represent
the number of defects per unit (taking on possible values of D, 1, 2, or 5 and the
factory nu

CL 202: Introduction to Data Analysis
Tutorial 10, 2015
1. For the CL202 midsem, the sample means of divisions S1 (60 students)
and S2 (59 students) were 24.84 and 25.12 respectively. The sample
variances for the two divisions were 91.199 and 107.47 respe

CS 215: Data Interpretation and
Analysis
Fall 2015
Instructors:
Ajit Rajwade
&
Suyash Awate
Where all do you analyze and
interpret data?
(1) In Medicine: Examples
Pathology reports,
Epidemiology studies
https:/ethnomed.org/clinical/tuberculosis/firlan
d

Introduction to Probability Theory (SI 417)
Department of Mathematics, IIT Bombay
July, 2015December, 2015
Problem set 4
1. Let X1 , X2 , . . . , Xr be independent random variables. Suppose Xi Bin(ni , p) for
1 i r. Find the probability mass function of (

Random Variables
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
Random variable: definition
Discrete and continuous random variables
Probability density function (pdf) and cumulative
distribution function (cdf)
Joint and conditional pdfs
Expectation

4
Suyash P. Awate
Transformation of a RV
Consider a RV X with PDF p(X).
Consider a transformed variable Y = g(X), where g() is an increasing function (we consider only the special case of
monotonic functions).
What is the PDF p(Y ) ?
Consider probabilit

Parameter Estimation
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
Concept of maximum likelihood estimation
Maximum likelihood estimates of the parameters of
various distributions
Concept of point estimate and confidence intervals
Estimator bias,

10
Suyash P. Awate
Multivariate Gaussian
Generalizes a univariate Gaussian.
Consider a vector random variable X = [X1 , X2 , , XD ]T . Nothing but a joint RV with d RVs. Represent as a d 1
vector.
Denition: The RV X has a multivariate (jointly) Gaussian

Discrete Probability
Fall 2015
Instructor:
Ajit Rajwade
Topic Overview
Some important terminology: sample space, event,
probability
Composition of events; mutual exclusion and
independence
Axioms of probability
Principles of counting
Conditional probabil

14
Suyash P. Awate
Bayesian Estimation
Thomas Bayes (18th-century mathematician and statistician)
Sir Harold Jeffreys (famous 20th-century mathematician and statistician) wrote that Bayes theorem is to the theory
of probability what Pythagorass theorem

Indian Institute of Technology, Bombay
CL202: Introduction to Data Analysis
Chemical Engineering
Tutorial 11, 2015
1. Chapter 8: 1 (In the problem consider the Indian Judicial System where the motto is: innocent
until proven guilty"), 2, 5, 7, 9, 25.
2. C