Formula Sheet-Probability and Random Processes

Download Formula Sheet-Probability and Random Processes

Post on 10-Apr-2015

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A simple formula sheet that lists basic and essential formulas for a first course in Probability and Random processes. It can also be used in examinations that allow students to bring only one A4 sized formula sheet.Contains basics of set theory, axioms of probability, probability distribution functions, stochastic convergence and a lot more.Can be edited or distributed freely, as long as the name of the original author is included in the document.If you like it, or dont like it, please drop in a comment.

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<p>Basics (Set theory, Axioms of Probability, Total Probability, Bayes Theorem) | , | | |</p> <p>, ! ! ! Distribution and Density Functions (Single Random Variable) 1, 0, , , 1 1 , 0, 1 ! , , 1 ,</p> <p>!</p> <p>!</p> <p>|</p> <p>|</p> <p>0, , |</p> <p>, ,</p> <p>,</p> <p>,</p> <p>One Function of Random Variable</p> <p>|</p> <p>,</p> <p>1 |</p> <p>,</p> <p>,</p> <p>, | |</p> <p>, 1,</p> <p>, ,</p> <p>,</p> <p>2</p> <p>1</p> <p>1</p> <p>, 1 , 1</p> <p>0, , ,</p> <p>, ,</p> <p>2 ,</p> <p>,</p> <p>4</p> <p>2 1</p> <p>,</p> <p>0</p> <p>Expectations</p> <p>|</p> <p>|</p> <p>|</p> <p>, | | |</p> <p>, |</p> <p>1</p> <p>1</p> <p>|</p> <p>Linearity of Expectation</p> <p>,</p> <p>0</p> <p>,</p> <p>Joint Distribution, Density and other relations(Functions of two random variables, Two functions of two random variables) , , =0 , , , , , : , , : | | , , , , , | | , , , , , , , , , , , , , 1 4 ,,</p> <p>1 2</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>1</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>, , ,</p> <p>,</p> <p>,</p> <p>, ,</p> <p>,</p> <p>,</p> <p>, , , ,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>1</p> <p>,</p> <p>Sequences of Random Variables . , , min ,,</p> <p>,</p> <p>|</p> <p>,</p> <p>,</p> <p>|</p> <p>| ,</p> <p>|</p> <p>,</p> <p>| , , min , , ,</p> <p>|</p> <p>0</p> <p>0</p> <p>0</p> <p>, |</p> <p>, , ,</p> <p>|</p> <p>0</p> <p>,,</p> <p>,</p> <p>, ,</p> <p>,</p> <p>Stochastic Convergence , , 1 ,</p> <p>1 ,</p> <p>Stochastic Processes ;</p> <p>,</p> <p>,</p> <p>|</p> <p>|</p> <p>|</p> <p>| ,</p> <p>,</p> <p>1 ! ,</p> <p>!</p> <p>! | ,</p> <p>1 , , ,, , ; , |</p> <p>, | |</p> <p>=</p> <p>0, ,</p> <p> ,</p> <p> , </p> <p>,</p> <p> ,</p> <p>,</p> <p>,</p> <p>, ,</p> <p>, ; , , ,</p> <p>,,</p> <p>;</p> <p>;</p> <p>,,</p> <p>,</p> <p>; , , ,</p> <p>,, , ; ,</p> <p>~</p> <p>,</p> <p> , ,,</p> <p>0,</p> <p>1</p> <p>,</p> <p>;</p> <p>, Systems with Stochastic Inputs , , , ,</p> <p>,</p> <p>,</p> <p>0,</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>0, ,</p> <p>,</p> <p>,</p> <p>, ,</p> <p>,,</p> <p>; ,,</p> <p>,</p> <p>,</p> <p>0 , )</p> <p>,,</p> <p>;</p> <p>| | ,</p> <p>,,</p> <p>0</p> <p>,</p> <p>,,</p> <p>,</p> <p>;</p> <p>, 0</p> <p>,,</p> <p>,</p> <p>, 1,1 2 , Integration (all integrals are w.r.t x) 1 1 | | Differentiation sin tan ln | |</p> <p>,</p> <p>,</p> <p>,</p> <p>, 2 1</p> <p>, , 1 ?</p> <p>,</p> <p>,</p> <p>,</p> <p>,</p> <p>, 1 2</p> <p>1</p> <p>1</p> <p>1</p> <p>1</p> <p>sin</p> <p>cos</p> <p>cos</p> <p>Matrix Operations</p> <p>cos</p> <p>Prepared by: Hammad Munawar (Institute of Avionics and Aeronautics, Islamabad, Pakistan) hammadmunawar@gmail.com</p> <p>| |</p> <p>1</p> <p>cos</p> <p>,</p> <p>(COPYRIGHT STATEMENT: May be used / distributed / edited freely, as long as the name of the original author is included)</p>

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