Are these notes free?

Yes. Fill in the short form on this page and the PDF downloads right away. There is no fee for the notes.

Are these official university notes?

No. These are original Uncodemy revision notes for Probability and Statistics, written in a handwritten style. They are not issued by AKTU or any other university, and they do not replace your textbook or class notes.

Which syllabus do these notes follow?

They follow the common B.Tech probability and statistics syllabus used by most Indian universities, and the probability and statistics part of GATE engineering mathematics. Your university may add topics such as ANOVA or the t-distribution in depth, so check your own syllabus.

Are these notes useful for data science?

Yes, as a base. Data science uses distributions, correlation, regression and hypothesis testing all the time. The notes cover the exam-level theory; a data science course then shows how to apply it on real data with Python.

Which distributions are covered?

Bernoulli, binomial, Poisson, geometric, uniform, exponential and normal, with their PMF or PDF, mean and variance in one table.

Can I get handwritten notes for another subject?

Yes. Browse the B.Tech notes hub for other subjects, or use the handwritten notes request page to ask for a subject that is not listed yet.

Probability and Statistics Handwritten Notes PDF

Key takeaways

Nine units, from mean and standard deviation to hypothesis testing.
One table with the PMF or PDF, mean and variance of seven standard distributions.
Solved examples on Bayes' theorem, binomial, Poisson, z-test and chi-square.
A quick guide to which test to use: z, t, chi-square or F.
Original Uncodemy revision notes; check your own university syllabus.

About these handwritten notes

These are original Uncodemy revision notes for Probability and Statistics, written in a clean handwritten style so they feel like a topper's notebook rather than a textbook. They are short on purpose: each unit gives the key definitions, formulas, a solved example or two and the points that are easy to forget.

The notes follow the common syllabus that most Indian B.Tech universities use for this subject, including universities that follow the AICTE model curriculum. They are not official notes from any university. Unit names, order and depth differ from one university to another, so check your own university syllabus and mark any topic that is missing before you rely on the notes for an exam. The notes focus on formulas, when to use each one, and solved examples that show the full working.

What's inside the probability and statistics notes

The notes have nine units. One line on each:

Unit 1: Basic statistics

Mean, median, mode, variance, standard deviation, coefficient of variation, and the effect of a change of origin and scale.

Unit 2: Probability basics

Sample space and events, addition and multiplication rules, mutually exclusive and independent events, conditional probability and counting.

Unit 3: Total probability and Bayes' theorem

The theorem of total probability and Bayes' theorem, with a tree-diagram tip and a solved example.

Unit 4: Random variables

Discrete and continuous random variables, PMF, PDF and CDF, and the rules for expectation and variance, with a die example.

Unit 5: Standard distributions

Bernoulli, binomial, Poisson, geometric, uniform, exponential and normal distributions in one table with their means and variances, plus solved binomial and Poisson examples.

Unit 6: Normal distribution

The standard normal variable Z = (X - μ)/σ and the area rule for 1, 2 and 3 standard deviations.

Unit 7: Joint distribution, correlation and regression

Covariance, Karl Pearson's correlation coefficient, the two regression lines and Spearman's rank correlation.

Unit 8: Sampling and hypothesis testing

Population and sample, the Central Limit Theorem, null and alternative hypotheses, Type I and Type II errors, a "which test?" table and solved z-test and chi-square examples.

Unit 9: Most asked questions (practice)

Ten practice questions across all the units.

How to revise probability and statistics with these notes

Learn the distribution table. The tip in the notes says to learn the Unit 5 table by heart. Mean and variance of binomial, Poisson and normal come up again and again.
Draw a tree for Bayes' problems. The notes suggest putting branch probabilities on the left and conditional ones on the right, then multiplying along each path. It turns a confusing question into simple arithmetic.
Standardise every normal question. Convert X to Z first, then use the table. Sketch the curve and shade the area you need.
Keep a formula card for regression. Write both regression lines, the correlation coefficient and the relation r² = b_yx x b_xy on one card.
Know which test to use. Large sample or known σ: z-test. Small sample with unknown σ: t-test. Goodness of fit or independence: chi-square. Two variances: F-test.
Check with tools. Compare your answers with the probability distribution calculator, the normal distribution calculator and the regression line calculator.

Exam focus: high-weightage topics

The tip at the end of the notes says GATE often asks Bayes' theorem, expectation and variance of standard distributions, and Poisson and normal probabilities. University papers add longer questions on fitting distributions, regression and tests of significance.

Topics worth extra time:

Descriptive statistics: mean, median, mode and SD of a grouped frequency table.
Bayes' theorem: the classic three-machine defective-item problem.
PDFs: find k so that f(x) = kx² on [0, 3] is a PDF, then a probability between two values.
Binomial: derive the mean and variance.
Poisson: fit a Poisson distribution to given data.
Normal: probabilities such as P(45 < X < 60) for X ~ N(50, 5²).
Correlation and regression: coefficient and both regression lines for a data set.
Testing: Type I and Type II errors, a chi-square goodness of fit test and the Central Limit Theorem.

Typical questions

These topics match the ten practice questions in the PDF. They are for practice and are not a prediction of your exam.

Who these notes are for

B.Tech students taking probability and statistics, often part of Engineering Mathematics 3 or 4, or a separate paper for CSE, IT and data science branches.
GATE aspirants revising the probability and statistics part of engineering mathematics. The GATE Data Science and Artificial Intelligence (DA) paper tests these topics in more depth.
Data science and analytics learners. Distributions, correlation, regression and hypothesis testing are the base of data analysis and machine learning, so these notes work as a refresher before an applied course.

Probability also helps in placement aptitude tests, where questions on dice, cards, coins and counting are common. Units 2 and 3 of the notes cover the rules you need for those questions.

For a broader view of what a data science course covers after this, see the Data Science syllabus PDF.

A simple 5-day revision plan

Day 1: Units 1 and 2. Descriptive statistics, probability rules and counting.
Day 2: Units 3 and 4. Bayes' theorem with tree diagrams, random variables, expectation and variance.
Day 3: Units 5 and 6. The distribution table and normal probabilities with the Z table.
Day 4: Units 7 and 8. Correlation, regression lines, sampling and the four tests.
Day 5: Solve the ten practice questions with a timer. Revise the distribution table one last time.

Common mistakes to avoid

Adding probabilities of events that are not mutually exclusive. Use P(A ∪ B) = P(A) + P(B) - P(A ∩ B) unless they cannot happen together.
Treating independent and mutually exclusive as the same. They are different ideas. Two events with non-zero probability cannot be both.
Forgetting that P(X = a) = 0 for a continuous variable. Probabilities come from areas, so use intervals.
Reading the wrong regression line. Use y on x to predict y and x on y to predict x.
Mixing up Type I and Type II errors. Type I rejects a true H0; Type II accepts a false H0.

Download Probability and Statistics Handwritten Notes PDF