CMI Data Science Entrance Books [Pdf] and Free Resources

Indian Institute of Technology is one of the top statistics departments in the country with great research and placement opportunities. It conducts an entrance exam for the aspirants who want to pursue a master's in Statistics called the IIT JAM MS Entrance Exam. To crack this exam, the best source of study materials is the right books. So, I am here to provide you the list of useful books for IIT JAM MS Entrance Exam preparation based on Syllabus.

A short note on the IIT JAM MS Entrance Exam: The MS programme offers advance level training in the theory, methods and applications of Statistics along with specialized training in selected areas of Statistics and allied fields. Depending on the area of specialization, students would be able to pursue an academic/research career in Statistics, Mathematics, Economics, Computer Science, and allied fields.

Free Mock Test

IIT JAM MS Entrance Exams Books according to the syllabus:

As mentioned in the website Entrance Exam mainly consists of 2 topics:

Mathematics (40%)
Probability and Statistics (60%)

Let's start with the Mathematics books required for IIT JAM MS Entrance Exam Preparation:

High School Mathematics - The mathematics part is super easy. So just be fluent in your 10+2 syllabus of mathematics and have a piece of sound knowledge in Calculus and Linear Algebra. Also, solve past year problems.

Although High School Mathematics part come less in the examination.

Let's discuss the books for Probability and Statistics Part, breaking it into different subsections according to the syllabus:

Combinatorics and Probability Theory
1. Book 1: (Chapter 1 - 8) -
  1. A First Course in Probability by Sheldon Ross
  2. Pdf File
2. Book 2: (Chapter 1 - 7)
  1. An Introduction to Probability and Statistics
3. Book 3: (Chapter 1 - 6) [For Quicker Purposes]
  1. Mathematical Statistics and Data Analysis by J.A.Rice
  2. Pdf File
Linear Algebra
1. Book: (Chapter 1 - 5, 7)
  1. Linear Algebra and Its Applications by Gilbert Strang
  2. Pdf File
  3. Lecture Series: Linear Algebra Lecture Series
Calculus and Real Analysis
1. Book: (Chapter 2, 4, 5, 7)
  1. Understanding Analysis by Stephen Abbott
  2. Pdf File
Statistics
1. Statistical Inference
  1. Book 1: (Chapter 7, 8, 9)
    1. Statistical Inference by Casella Berger
    2. Pdf File
  2. Book 2: Chapter (8,9)
    1. Mathematical Statistics and Data Analysis by J.A.Rice
    2. Pdf File

5. A book named "Solutions to IIT JAM for Mathematical Statistics" by Amit Mishra and Mohd. Arshad covers previous year solutions till 2018. You can consider buying that book for your IIT JAM MS Preparation.

Other Useful Resources

IIT JAM Statistics Crash Course for 2022

Early bird Registration is Going On. Classes start from 1st week of October, 2021.

ISI MStat Entrance 2021 Problems and Solutions PSA & PSB

This post contains ISI MStat Entrance PSA and PSB 2021 Problems and Solutions that can be very helpful and resourceful for your ISI MStat Preparation.

Download Paper

PSA Paper

PSB Paper

ISI MStat 2021 PSA Answer Key and Solutions

Click on the links to learn about the detailed solution. (Coming Soon)

49 (Rolle's Theorem)

2. 2 (4 - number of linear constraints)

3. k = 2 (a = -d, and form a biquadratic which has two real solutions)

4. 0 (divide by $x^4$, use $\frac{sinx}{x}$ limit result)

5. $\frac{p}{q}$ must be a rational number. (The product must be a rational number.)

6. $\alpha = 1, \beta =1$ (Use sandwich theorem on an easy inequality on ceiling of x)

7. $\frac{2n}{n+1}$ (Use geometry and definite integration)

8. $2+ \sqrt{5}$ (Just write down the pythagoras theorem in terms of the variables and solve)

9. 10 (Use the roots of unity)

10. $\frac{3}{8}$ (Find out the cases when it is non zero, and use classical probability)

11. $\frac{(n+1)^n}{n!}$ (Use ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$)

12. $P(\pi)$ is even for all $\pi$. (Observe that there is one more odd than number of evens, so there will be one odd-odd match)

13. is equal to 12. (The $i,j$th element is $a_{ii}b{ij}c{jj}$. Use gp series then.)

14. 160 (Use the fact any permutation can be written as compositions of transpositions. Observe that the given condition is equivalent to that 2 transpositions are not possible)

15. $m_t < \infty$ for all $t \geq 0$ (All monotone functions are bounded on [a,b])

16.$H(x) = \frac{1-F(-x)+ F(x)}{2}$ (If $F(x)$ is right continuous, $F(-x)$ is left continuous.).

17. $\frac{1}{25}$ (Use the distribution function of $\frac{X}{Y}$)

18. 3 (Find the distribution of order statistic, and find the expectation)

19. (II) but not (I) (If $F(x)$ is right continuous, $F(-x)$ is left continuous.).

20. $20\lambda^4$ (Use gamma integral to find the $E(X_{1}^4)$.)

21. The two new observations are 15 and 5. (Use the condition to find two linear equations to find the observations).

22. It is less than 2. (Use the beta coefficients in terms of sample covariance and sample variance, and compare)

23. 4:3 (Use Bayes' Theorem)

24. The two-sample t-test statistic and the ANOVA statistics yield the same power for any non-zero value of $\mu_1 - \mu_2$ and for any $n,m$. (Both the test statistic are one to one function of one another)

25. t³-1 - 2(t-1)

26. $\frac{2 \sum_{i=1}^{n} X_i}{n(n+1)}$ (Use the invariance property of MLE)

27. $Y_1^2 + Y_2^2 + Y_1Y_2$ (Write the bivariate normal distribution in terms of $Y_1, Y_2$ and use Neyman Factorization Theorem.)

28. can be negative (Simson's Paradox)

29. $2z$ (There are three random variables, $N$ = stopping time to get $Y=1$, $Y$ and $X$. Use the conditioning properly. Take your time)

30. $\frac{40}{3}$ (Use the property that Poisson | Poisson in the given problem follows Binomial)

ISI MStat 2021 PSB Solutions

Coming soon.

ISI MStat PSB 2021 Problem 1

Solution

ISI MStat PSB 2021 Problem 2

Solution

ISI MStat PSB 2021 Problem 3

Solution

ISI MStat PSB 2021 Problem 4

Solution

ISI MStat PSB 2021 Problem 5

Solution

ISI MStat PSB 2021 Problem 6

Solution

ISI MStat PSB 2021 Problem 7

Solution

ISI MStat PSB 2021 Problem 8

Solution

ISI MStat PSB 2021 Problem 9

Solution

Please suggest changes in the comment section.

Cheenta Statistics Department
ISI MStat and IIT JAM Training Program

How to prepare for CMI Data Science Examination?

Is Multivariate Limit = Iterated Limit? Multivariate Limit Demystified

Is Multivariate Limit equal to Iterated Limit?

The multivariate limit is really akin to the univariate limit. But, how can we explain that?

However, We discuss the following aspects in this regard.

📌 Firstly, we discuss the ideas of proving and disprove Univariate Limits.
📌 Then, come Multivariate Limits - How to prove and disprove?
📌 Thereafter, Iterated Limits appear - Understanding and Geometry.
📌 Hence, we discover Relationship between Multivariate Limits and Iterated Limits.
📌 We end with Food for Thought.

Iterated Limits are a bypass. Do they really explain the Multivariate Limit?

We discover a rich relationship between the two. We give all the cases possible between multivariate limits and iterated limits.

Hints, Solution, and More

Write down the $ \epsilon - \delta$ definition of multivariate limit.
How can you disprove the existence of a multivariate limit?
Think of some useful ways to prove the existence of a multivariate limit?
What are the iterated limits?
How are they connected to the multivariate limit?
Let's explore the connection in the video.
Don't forget the food for thought.

Enjoy the video

Build your foundations.

Ace your Exams.

Learn. Enjoy. Practice. Repeat.

Firstly, Multivariate Limit - No. Iterated Limits - No.
Secondly, Multivariate Limit - No. Iterated Limits - Yes and Different.
Therefore, Share one example that follows the conditions of Moore Osgood's Theorem and the results are true.
Thus, Give one example that doesn't follow the conditions of Moore Osgood's Theorem, and the results are not true.
Finally, Give one example that follows the result of Moore Osgood's Theorem, but doesn't follow the conditions.

Some Useful Links:

Stay Tuned!

When Maximum Likelihood = Method of Moments?

Is Maximum Likelihood = Method of Moments?

Maximum Likelihood Estimation is an algorithm to find a reasonable estimator. Personally, it really woos my mind - simple and yet so beautiful. Method of Moments is simpler. It doesn't woo me :p. However, still, they have a lot of similarities. Thus, we have set off to explore them. Finally, we ask for a lot of food for thought. After all, we are all explorers at heart.

We ask "Is MLE = MOM? If not, when?"

We discover a rich relationship between the two. We discover the score function and so much more exciting.

Hints, Solution, and More

Find out examples where the estimates of Maximum Likelihood and Method of Moments are same.
Find out examples where the estimates of Maximum Likelihood and Method of Moments are not same.
Prove that Maximum Likelihood Estimation is same as solving $\sum_{i=1}^{n} \frac{\partial}{\partial \theta} \log f\left(X_{i} \mid \theta\right)=0$.
Prove that Method of Moments Estimation is same as solving $(\frac{1}{n} \sum_{i=1}^{n} X_{i}^{k}-\mu_{k}(\theta)=0)$.
Let's explore the connection in the video.
Don't forget the food for thought.

Enjoy the video

Build your foundations.

Ace your Exams.

Learn. Enjoy. Practice. Repeat.

Above all, prove that $E(h(X, \theta))=0$ for Maximum Likelihood Estimation and Method of Moments Estimation.
In addition, what is the intuition of the score function? Thus, we ask what is the intuition of the variance of the score function?
Do you think that method of moments and maximum likelihood estimate is equal for the exponential family?
As a result, we explore a one-parameter family. Thus, can you find out the pdf of the distributions for which the two estimates will be the same?
However, can you comment on the sufficient statistic, if the estimates are the same?

Some Useful Links:

ISI MStat 2020 PSB Problem 9 | Discussion & Solution

ISI MStat 2020 PSB Problem 9

This post discuses the problem 9 of the ISI MStat 2020 PSB Entrance Exam.

A finite population has $N$ units, with $x_{i}$ being the value associated with the $i^{\text {th }}$ unit, $i=1,2, \ldots, N$. Let $\bar{x}{N}$ be the population mean.

A statistician carries out the following experiment.

Step 1: Draw a SRSWOR of size $n({1}$ and denote the sample mean by $\bar{X}{n}$.

Step 2: Draw a SRSWR of size $m$ from $S{1}$. The $x$ -values of the sampled units are denoted by {$Y_{1}, \cdots, Y_{m} $}.

Hints, Solution, and More

$\tilde{X}$ follows SRSWOR on population with mean $\mu$.
$E_{\tilde{X}}\left(\bar{X}{n}\right)=\mu$
$\tilde{Y} \mid \tilde{X}$ follows SRSWR on $\tilde{X}$ with mean $\bar{X}{n}$
$E_{\tilde{Y} \mid \tilde{X}}\left(\hat{T}{m}=\bar{Y}{m}\right)=\bar{X}_{n}$
Use the smoothing property of expectation and variance.

Do subscribe to our channel to get instant notification of Live Session, so that you can join us live in the master classes!

Build your foundations.

Ace your Exams.

Learn. Enjoy. Practice. Repeat.

What will be the case for SRSWR?
Can you prove the increasing variance idea without doing the variance computation?
Prove that taking any sampling scheme in the second step, which is unbiased for step 2, will also follow the results, proved above.
Do practice the SRSWR and SRSWOR variance computation.

Some Useful Links:

Is MLE always a function of a Sufficient Statistic?

MLE is an algorithm to find a reasonable estimator (personally, it really woos my mind - simple and yet so beautiful.).

Now, well - Life is hard. People has devised ways to check if an esimator is good or not - why will they care I like it or not.

So, they have developed Small Sample Properties and Large Sample Properties to do the quality control of MLE.

This post tests the flamboyancy of MLE is terms of the idea of "Sufficiency".

We ask "Is MLE sufficient? How is MLE and Sufficiency related?"

We discover a rich relationship between the two. Again, MLE wins my heart. Does it win yours? Check with the hints and the solution.

Hints, Solution, and More

Use Neymann Factorization Theorem to prove that MLE is a function of a Sufficient Statistic $T$ .
Write the Likelihood of the data is terms of $T$ and progress towards the proof.
Now, take a sample from Uniform ($\theta,\theta +1$).
Now, observe that MLE is not unique and find a MLE which is not a function of $T$ - a small but creative step.
Look out for the Food for Thought.

Do subscribe to our channel to get instant notification of Live Session, so that you can join us live in the master classes!

Build your foundations.

Ace your Exams.

Learn. Enjoy. Practice. Repeat.

Is MLE a sufficient statistic?
Is MLE consistent?
IS MLE a complete sufficient statistic?
Is MLE asymptotically normal?
Is MLE UMVUE?
What if the underlying distribution is Exponential Family?

Some Useful Links:

ISI MStat 2020 PSB Problem 6 Problem & Solution

ISI MStat 2020 PSB Problem 6

This post discuses the problem 6 of the ISI MStat 2020 PSB Entrance Exam.

Suppose individuals are classified into three categories $C_{1}, C_{2}$ and $C_{3}$ .

Let $p^{2},(1-p)^{2}$ and $2 p(1-p)$ be the respective population proportions, where $p \in (0,1)$ . A random sample of $N$ individuals is selected from the population and the category of each selected individual recorded.

For $i=1,2,3$ , let $X_{i}$ denote the number of individuals in the sample belonging to category $C_{i}$ . Define $U=X_{1}+\frac{X_{3}}{2}$ .

Is $U$ sufficient for $p$ ? Justify your answer.
Show that the mean squared error of $\frac{U}{N}$ is $\frac{p(1-p)}{2 N}$.

Hints, Solution, and More

Prove that the joint distribution of $(X_1,X_2,X_3)$ follows Multinomial Distribution.
Write the Likelihood of the data.
Use Neymann Factorization to prove the sufficiency of $U$.
Show that $\frac{U}{N}$ is unbiased.
Show that $2U$ follows Binomial Distribution.

Do subscribe to our channel to get instant notification of Live Session, so that you can join us live in the master classes!

Build your foundations.

Ace your Exams.

Learn. Enjoy. Practice. Repeat.

Prove that $\frac{U}{N}$ is the UMVUE of $p$.
Find the minimal sufficient and complete statistic of $p$.
For other Food for Thought, refer to the youtube video for full solution.

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How to Prepare for IIT JAM MS Statistics Exam?

IIT JAM MS Programme is the postgraduate statistics program taught by IIT. The IIT JAM MS Entrance Examination is held from January - February(the time is not fixed for next year due to COVID-19).

IIT JAM MS Examination entirely focuseses on Objective Problems.

The exam scoring pattern is the following:

The examination is of 3 hours duration. There are a total of 60 questions carrying 100 marks. The entire
paper is divided into three sections, A, B and C. All sections are compulsory. Questions in each section are
of different types.
Section – A contains a total of 30 Multiple Choice Questions (MCQ). Each MCQ-type question has four
choices out of which only one choice is the correct answer. Questions Q.1 – Q.30 belong to this section
and carry a total of 50 marks. Q.1 – Q.10 carries 1 mark each and Questions Q.11 – Q.30 carries 2 marks
each.
Section – B contains a total of 10 Multiple Select Questions (MSQ). Each MSQ type question is similar
to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the
four given choices. The candidate gets full credit if he/she selects all the correct answers only and no
wrong answers. Questions Q.31 – Q.40 belong to this section and carry 2 marks each with a total of 20
marks.
Section – C contains a total of 20 Numerical Answer Type (NAT) questions. For these NAT-type
questions, an answer is a real number that needs to be entered using the virtual keyboard on the monitor.
No choices will be shown for these types of questions. Questions Q.41 – Q.60 belong to this section and
carry a total of 30 marks. Q.41 – Q.50 carries 1 mark each and Questions Q.51 – Q.60 carries 2 marks each.
In all sections, questions not attempted will result in zero marks. In Section – A (MCQ), a wrong answer will
result in NEGATIVE marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer.
For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section – B (MSQ), there
are NO NEGATIVE and NO PARTIAL marking provisions. There is NO NEGATIVE marking in
Section – C (NAT) as well.

Let me discuss a little bit about the syllabus.

The Mathematics part involves

Real Analysis
Linear Algebra

The Broad Topics in Proabability and Statistics are

Probability
Estimation Theory

How to Prepare for IIT JAM MS Statistics Entrance?

I know you are waiting for this part. The truth is that, yes you can prepare yourself alone if you are enough motivated about solving problems on chance and data.

But the main problem is people don't know where to start. I will try to help you do so, in this post.

What will be my Focus?

Here, focus means with respect to your content. You have to be fully focussed on a single source for learning your topics. The best source is a book, where you can get it all. The easiest way in this information-rich world is to get lost. So, try to focus.

I always referred myself two books and therefore I recommend you to do so.

A First Course in Probability by Sheldon Ross
Mathematical Statistics and Data Analysis by John.A.Rice.

Just take this as the bible and you will do wonders. I can't guarantee you a position in the IIT JAM MS Statistics program, but I can guarantee you an enjoyable process of learning chance and data, which will put you in the top 10% of those in the preparation. The rest is left to luck.

For the Mathematics, portion be fluent in your 10+2 syllabus of mathematics and have a sound knowledge in Calculus and Linear Algebra.

Preparation Tips six months before the Exam:

I believe that majority are in this window. So, I strictly against any windowless than six months for the beginning of your preparation. It shows your attitude towards life and even if you get into IIT, it will cost you big somewhere in your life. So, stop procrastinating. Don't believe in that stuff that procrastinating makes you creative. That's a myth.

Start solving your past year's paper.
Make a Separate Copy
Try to figure out what you can solve and what you cannot.
Take this feedback and try to work on your weak areas.
Try to take some guidance from some expert like seniors, teachers, etc ( Not Necessary )
Repeat.

All the best!

See what our experts have to say

How to prepare for IIT JAM MS 2021 just 1 - 2 weeks before the exam?

A Preparation Strategy - A Data Analysis

Why Cheenta for IIT JAM MS Statistics Entrance Exam Preparation?

Suppose, you get into ISI / IIT or don't get into ISI / IIT after your years of hard work. We believe, that you shouldn't work hard. Working hard means, you are doing something hard against something. You are in this path of study, only because you are in love with data. Even if you are not, then try to fall in love with the path of learning and crunching information from data. We are there to help you.

Cheenta will just help you organize your study program. We will ensure that you are on the right track and don't get off track with so much information out there. We give you a study plan, which will help you complete the tasks one step at a time. We will discuss problems from past years in accordance with the theory.

Above all, we will help you to learn the applications of data and the theory you are learning. We believe, statistics and data science without applications is as boring as a kite without the thread.

So, with every bit of knowledge you gain, we will teach you the coding perspective of it.

For example You are learning Probability 1 in our curriculum and you are introduced to the idea of equally likely sampling/selection. Now the natural question comes, how do I select equally likely objects by a machine? It is just a simple line of code.

sample(10,2)
5 8

From, this will arise questions, does this give equally likely in both the steps or it is SRSWOR? Our curriculum is based on the principles of ancient india. We are all seekers. We seek more and more. That is the moto of Cheenta.

If you believe, you can do these by yourself, you can do self study, rather than joining our program. You will get much more freedom.

For more information about our coursework, you can click here.

All the best.

Stay Tuned! Stay Blessed!

IIT JAM Statistics Entrance Exam books based on Syllabus

Free Mock Test

IIT JAM MS Entrance Exams Books according to the syllabus:

As mentioned in the website Entrance Exam mainly consists of 2 topics:

Mathematics (40%)
Probability and Statistics (60%)

Let's start with the Mathematics books required for IIT JAM MS Entrance Exam Preparation:

Although High School Mathematics part come less in the examination.

Let's discuss the books for Probability and Statistics Part, breaking it into different subsections according to the syllabus:

Combinatorics and Probability Theory
1. Book 1: (Chapter 1 - 8) -
  1. A First Course in Probability by Sheldon Ross
  2. Pdf File
2. Book 2: (Chapter 1 - 7)
  1. An Introduction to Probability and Statistics
3. Book 3: (Chapter 1 - 6) [For Quicker Purposes]
  1. Mathematical Statistics and Data Analysis by J.A.Rice
  2. Pdf File
Linear Algebra
1. Book: (Chapter 1 - 5, 7)
  1. Linear Algebra and Its Applications by Gilbert Strang
  2. Pdf File
  3. Lecture Series: Linear Algebra Lecture Series
Calculus and Real Analysis
1. Book: (Chapter 2, 4, 5, 7)
  1. Understanding Analysis by Stephen Abbott
  2. Pdf File
Statistics
1. Statistical Inference
  1. Book 1: (Chapter 7, 8, 9)
    1. Statistical Inference by Casella Berger
    2. Pdf File
  2. Book 2: Chapter (8,9)
    1. Mathematical Statistics and Data Analysis by J.A.Rice
    2. Pdf File

Other Useful Resources

IIT JAM Statistics Crash Course for 2022

Early bird Registration is Going On. Classes start from 1st week of October, 2021.