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The concept of joint probability distributions of random variables and their correlation. The joint probability distribution of an exponential random variable pair, a pair of erlang random variables, and a pair of dependent random variables. The document also discusses the correlation and covariance between random variables and their relationship. Examples of joint probability distributions and their corresponding trajectories on the joint pdf.

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Download Joint Probability Distributions & Correlation in Stochastic Processes and more Slides Probability and Stochastic Processes in PDF only on Docsity! CS723 - Probability and Stochastic Processes docsity.com Lecture No. 19 docsity.com Joint PDF of two exponentially distributed random variable X and Y
Joint PDF of two Erlang type random variable X and ¥
Pair of Dependent RV’s fXY(x,y) defined for (x,y) ε [0,10]x[0,10] fXY(x,y) = K(2x + y) = (2x + y)/1500 fX(x) = (5 + 2x)/150 & fY(y) = (10 + y)/150 docsity.com Trajectories on Joint PDF 0 1 2 3 4 5 6 7 8 9 10 docsity.com Pair of Dependent RV’s fXY(x,y) defined for (x,y) ε [0,∞)x[0, ∞) fXY(x,y) = K( e-x/10 e-y/20 e-xy/30) Portion of trajectories are shown 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 docsity.com Pair of Gaussian RV’s fXY(x,y) defined for (x,y) ε (-∞, ∞)x(-∞, ∞) fXY(x,y) = K(e-αx 2 e-βy2 e-γxy) = K e-(αx2 + βy2 + γxy) docsity.com