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Chap. 5: Joint Probability Distributions

Chap. 5: Joint Probability Distributions Probability modeling of several RV s We often study relationships among variables. Demand on a system = sum of demands from subscribers (D = S1 + S2 + . + Sn). Surface air temperature & atmospheric CO2. Stress & strain are related to material properties; random loads; etc. Notation: Sometimes we use X1 , X2 , ., Xn Sometimes we use X, Y, Z, etc. 1. Sec : Basics First, develop for 2 RV (X and Y). Two Main Cases I. Both RV are discrete II. Both RV are continuous I. (p. 185). Joint Probability Mass Function (pmf) of X and Y is defined for all pairs (x,y) by p( x, y ) P( X x and Y y ). P( X x, Y y ).

6 II. Both continuous (p. 186) A joint probability density function (pdf) of X and Y is a function f(x,y) such that • f(x,y) > 0 everywhere f and ³³ A P[( X, Y) A] f ( x, y)dxdy

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