PowerPoint Presentation

Ali Zar 14093122-027Aqeel Haider 14093122-017Shahbaz Sharif 14093122-010Electrical Engineering, 5th University of Gujrat, Hafiz Hayat campus, GujratGroup members

Topic of representationRandom variables for discrete case

Outlines of topicRandom variablesDistribution/ cumulative function DF/ cdfProbability density functionJoint distributionExpectation of random variables

Random variablesSuch a numerical quantity whose value is determined by the outcome of a random experiment, is called a random variable. Arandom variableis a variable that is subject to randomness, which means it can take on different values.A random variable is also called chance variable, and is abbreviated as r.v.The random variables are denoted by capital letters as X, Y, Z and values taken by them as x,y,z.Two types of r.v :The discreteThe continuous

Example

Distribution/ cumulative function DF/ cdf

Example Suppose, three coins are tossed and x is number of tails. Find probability distribution and construct its graph.

Joint distribution

How to calculate?

Expectation of random variables

How to calculate?

Applications in Electrical Engineering

Application 1If we want to find probability of circuits accepted or not.if number of given integrated circuit would be accepted or rejected we use discrete PMF.

Application 2If we want to find number of semiconductor wafers that need to be analyzed in order to detect a large particle of contamination in p-type or n-type material or in doping material we use random variables or discrete random variable.

Application 3If we have number of circuit and we need the probability to test circuit to be defective and non-defective we use discrete variable distribution to find the number of defective and non-defective circuits.

Applications in Civil Engineering

Application 1If we want to find load on a specific point in a beam we can use discrete functions to find loading at each point on a beam.Suppose a loading on a long, thin beam places mass only at discrete points. The loading can be described by a function that specifies the mass at each of the discrete points. Similarly, for a discrete random variable X, its distribution can be described by a function that specifies the probability at each of the possible discrete values for X.

Application 2Statisticians use sampling plans to either accept or reject batches or lots of construction material. Suppose one of these sampling plans involves sampling independently 10 items from a lot of 100 items in which 12 are defective.

Applications in Business

Application 1In any business firm there is a communication system with certain number of lines to communication data and voice communication. If we need to know the probability of how many lines are working at one time we use discrete variables.

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