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- 1Chapter 5 - Bivariate Discrete Random Variables The joint probability mass function (PMF) is given by? The joing cumulative distribution function (CDF) is given by?px,y(x,y) = Pr(X=x,Y=y)
Fx,y(x,y) = Pr(X - 2Chapter 5 - Marginal PMF's and Independent random variables The marginal PMF of X is? The marginal PMF of Y is? X and Y are independent if?px(x) = SIGMA[y](Pr(X=x,Y=y)
py(y) = SIGMA[x](Pr(X=x,Y=y)
Pr(X=x,Y=y) = P(X=x)Pr(Y=y) - 3Chapter 5 - Conditional distributions The conditional distribution of X given Y=y is? The conditional distribution of Y given X=x is? X and Y are independent if?px¦y(x¦y) = Pr(X=x¦Y=y) = [Pr(X=x,Y=y)]/Pr(Y=y)
py¦x(y¦x) = Pr(Y=y¦X=x) = [Pr(X=x,Y=y)]/Pr(X=x)
px¦y(x¦y) = px(x) or py¦x(y¦x) = py(y) - 4Chapter 5 -The sum of two discrete random variables For any X any Y the PMF of the random variable X+Y is? If X and Y are independent then what is the PMF of the random variable X+Y?px+y(z) = SIGMAx[px,y(x,z-x)] or
px+y(z) = SIGMAy[px,y(z-y,y)]
px+y(z) = SIGMAx[px(x)py(z-x)] or
px+y(z) = SIGMAy[py(y)px(z-y)]
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- Karteikarten am Ohne Titel, erstellt von Cara Wales am 27/01/2016.
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