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Exponential Random Variable-Probability and Stochastic Processes-Lecture Slides, Slides of Probability and Stochastic Processes

Institute of Mathematics and ApplicationsProbability and Stochastic Processes

Probability and Stochastic Processes course is part of basic science because of its usage in many fields. Most of its concepts are explained by using common examples like coin toss, rolling dice, deck of cards. Prof Mayur Somnath delivered this lecture to discuss Exponentially, Distributed, Failure, Red, Green, Survives, Months, Excessive, Survival

Typology: Slides

2011/2012

Uploaded on 08/04/2012

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CS723 - Probability
and
Stochastic Processes
CS723 - Probability
and
Stochastic Processes
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Download Exponential Random Variable-Probability and Stochastic Processes-Lecture Slides and more Slides Probability and Stochastic Processes in PDF only on Docsity!

CS723 - Probability

and

Stochastic Processes

CS723 - Probability

and

Stochastic Processes

  • Lecture No. 15Lecture No.

Exponential Random VariableExponential Random Variable^0

PDF's of a family of exponetially distributed random variables

CDF's of PDF's given above

Failure of a TV SetFailure of a TV Set

Red

TV fails during the first 6 months

Green

TV fails after 2 years i.e. it

survives for 2 years

Red

TV fails during the first 6 months

Green

TV fails after 2 years i.e. it

survives for 2 years

Memory-less Exponential RVMemory-less Exponential RV

Another Example of Cont. RVAnother Example of Cont. RV^0

PDF's of a family of continuous random variables with pdf f

X

(x) =

2

xe

x

CDF's of PDF's given above. They are F

X

(x) = 1 - e

x

x e

 x

Gaussian Random VariableGaussian Random Variable

PDF's of a family of Gaussian random variables

CDF's of PDF's given above