**PTSP Notes:** Are you always confused about which website to trust with information about your marks? Are you shuffling between websites to find information? Are you confused and still don’t have your basics clear? Are you struggling to find the right study material for PTSP Unit Wise Notes Pdf? Here you can find all the information that you have been looking for. You will find all the Probability Theory and Stochastic Processes Notes Pdf and PTSP study material you require along with the previous year’s question papers on this site.

Student can also read PTSP Lecture Notes Pdf for Preparation.

## What is PTSP?

- Probability Theory and Stochastic Processes (PTSP) is a subject required in B.tech.
- It is a semester wise examination conducted by university students.

### How do we help you?

- We provide you with ample PTSP Notes Pdf Download, jotted down in genuine language for your better understanding.
- We also offer you PTSP Handwritten Notes along with previous year’s question papers.
- Apart from that, in this PTSP Unit Wise Notes Pdf, we jot down a few questions that have been repeatedly asked during the past years separately as these questions hold more importance.
- Further, we also resolve specific questions for you so you can get an understanding of how to frame your answers.
- We also provide PTSP JNTU Notes with multiple links to pdfs that may help you. Overall, we provide you with enough information and other study material to help you ace your exams and prepare for them without much hassle.

In due course of this article, we will tell you all about PTSP and prepare for it. On this website, You will find all relevant Probability Theory and Stochastic Processes Notes Pdf. All these will be available for free download and accessible on this page for students, especially for the ones who are preparing for the PTSP exams. It can get challenging to prepare for such exams, which is why we don’t charge you any amount and all your PTSP Notes for preparation are available on this website for absolutely no cost. This way, you can score maximum marks and resources or are also easily accessible.

Some questions are repeatedly asked during exams. It is because those concepts hold maximum importance. To save you some time from going through several websites, we have compiled all critical questions for you. Because if you sit and go through every single site, then you will waste your time. Hence, taking more time to prepare for the exam.

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### List of Some Crucial Important Questions

The list of some crucial questions is attached below:-

- A discrete random variable can be defined in a continuous sample space whether it is true or false. Give an example to support your claim.
- Write the conditions to be satisfied by a function to be a random variable the probability density function’s properties.
- Define the terms outcome, event, sample space, mutually exclusive events. Now consider the experiment of rolling these two fair dice simultaneously and represent its sample space. Also, give examples of the terms mentioned above related to this experiment.
- State and prove Bayes Theorem.
- Define the autocorrelation function of a random process. Write properties of the autocorrelation function of a WSS process and prove any three of them.
- Gain the Moment generating of function for a uniformly distributed random variable.
- Obtain the variance of the Rayleigh random variable.
- Find the Moment generating function of a uniform random variable distributed over (A, B) and find its first and second moments about the Moment generating function’s origin.
- Derive the expression for the Cross Spectral Density of the input Process X(t) and the output process Y(t) of an LTI system in terms of its Transfer function.

Preparation of other concepts and questions is also very important, but it is also essential to keep in mind that your basics have to be clear before going into a subject’s depth. These questions will help you get your basics healthy.

Further, you will learn about the unit wise syllabus of PTSP.

### Unit wise Syllabus of PTSP

UNIT |
COURSE |

Unit 1 | Probability: Probability introduced through Sets and Relative Frequency, Experiments and Sample Spaces, Discrete and Continuous Sample Spaces, Events, Probability Definitions, and Axioms, Probability as a Relative Frequency, Joint Probability. Conditional Probability, Mathematical Model of Experiments, Total Probability, Bayes’ Theorem, Independent Events. |

Unit 2 | Random Variable: Definition of a Random Variable, Conditions for a Function to be a Random Variable, Discrete, Continuous and Mixed Random Variables, Distribution and Density functions and their Properties – Binomial, Poisson, Uniform. Gaussian, Methods of defining Conditional Event Conditional Density, Exponential, Rayleigh and Conditional Distribution, Properties. |

Unit 3 | Operation on One Random Variable: Expectations Introduction, Expected Value of a Random Variable, Function of a Random Variable, Moments about the Origin Central Moments, Variance, and Skew, Chebycher’s Inequality, Characteristic Function, Moment Generating Variable. Function, Transformations of a Random Variable: Non-Monotonic Transformations of Continuous Random Variable. Monotonic Transformations for a Continuous Random Variable, Transformation of a Discrete Random. |

Unit 4 | Multiple Random Variables: Vector Random Variables, Joint Distribution Function Properties of Joint Distribution, Marginal Distribution Functions. Conditional Distribution and Density Point Conditioning, Conditional Distribution and Density – Interval conditioning, Statistical Independence, Sum of Two Random Variables, Sum of Several Random Variables, Central Limit Theorem (Proof not expected), Unequal Distribution, Equal Distributions. |

Unit 5 | Operations on Multiple Random Variables Expected Value of a Function of Random Variables: Joint Moments about the Origin, Joint Central Moments, Joint Characteristic Functions, Jointly Gaussian Random Variables: Two Random Variables case. N Random Variable case, Linear Transformations of Gaussian Random Variables, Transformations of Multiple Random Variables, Properties. |

Unit 6 | Stochastic Processes – Temporal Characteristics The Stochastic Process Concept, Classification of Processes. Deterministic and Nondeterministic Processes, Distribution and Density Functions. Concept of Stationarity and Statistical Independence, First-Order Stationary Processes, Second-order, and Wide-Sense Stationarity, Nth Order and Strict-Sense Stationarity, Mean-Ergodic Processes. Correlation-Ergodic Processes, Time Averages and Ergodicity, and its Properties. Autocorrelation Function, Cross-Correlation Function, and its Properties. Linear System Response of Mean and Mean-squared Value. Covariance and its Properties, Autocorrelation Function, Cross-Correlation Functions, Gaussian Random Processes, Poisson Random Process. |

Unit 7 | Stochastic Processes – Spectral Characteristics, Search document power Spectrum: Properties, Relationship between Power Spectrum and Autocorrelation Function, Cross-Power Density Spectrum, Properties, Relationship between Cross-Power Spectrum and Cross-Correlation Function, Spectral Characteristics of System Response: Power Density Spectrum of Response, Cross-Power Spectral Density of Input and Output of a Linear System. |

Unit 8 | Noise- Types of Noise: Resistive (Thermal) Noise Source, Shot noise, Extraterrestrial Noise, Arbitrary Noise Sources, White Noise, Narrowband Noise: In-phase and quadrature-phase components and its Properties, Modeling of Noise Sources, Average Noise Bandwidth. Sufficient Noise Temperature, Average Noise Figures, Average Noise Figure of cascaded networks. |

### List of Some Books

Here is the list of some books you can refer to –

- Random Variables & Random Signal Principles, Probability – Peyton Z. Peebles, 4th edition, 2001.
- Probability. Random Variables and Stochastic Processes- Athanasios Papoulis and S. Unnikrishnan Pillai, 4th edition.
- Principles of Communication systems-H.Taub, Donald L. Schilling, Goutam Saha, 3rd edition, 2007.

### FAQs on PTSP Notes

Question 1

What is PTSP?

- Probability Theory and Stochastic Processes (PTSP) is a subject required while you are pursuing your B.Tech.
- It is a mandatory examination that you would require to sit for.

Question 2.

How to prepare for PTSP?

- The best way to prepare for PTSP is going through the previous year’s question papers and notes.
- It is also essential to closely follow the syllabus.

Question 3.

Where can I find appropriate study material?

- Our website takes care of all your requirements in regards to the study material required.
- We provide previous year question papers, notes, updated syllabus, and also highlight the most important questions for you.

Question 4.

What are the tips to keep in mind while preparing for PTSP exams?

- The first step towards this is understanding the syllabus in details, do you can proceed unit wise
- The next step is going through notes and also preparing your own notes.
- Lastly, solve past year question papers.

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### Conclusion on PTSP Notes

We strive to make studying a better experience for students. We want to reach out to each one of you and congratulate you for doing so well in life. Are you looking for different study material? Question papers and PTSP Notes Download can become quite a task sometimes. So, we thought, why not make this job easier for you, which is why we have compiled all resources available on the internet in one place, on our website.

You will find books you can refer to, various question papers and solutions, PTSP Lecture Notes Pdf, and a detailed syllabus.

Our website is the one-stop solution for Probability Theory and Stochastic Processes Notes Pdf, as we work hard every day to get all resources ready for you. And all this at absolutely no cost.

We hope all of you pass your exams with flying colours, and we also hope that we were able to be of some help to you.