16.322 Stochastic Estimation and Control, Fall 2004 Prof vander velde Probability distribution function(or cumulative probability function) F(x)=P(X sx), where x is the argument and X is the random variable name Properties F(-∞)=0 F(∞)=1 0≤F(x)≤1 F(b)≥F(a),ib>a F(x Continuous random variable F(x) Discrete random variable An alternate way to characterize random variables is the probability density functio on: f(x)=“f(x f(x)≥0,x f(x)=F(-∞)+|f(an)d f(u)du Page 2 of 716.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde Probability distribution function (or cumulative probability function) Fx ( ) = PX ( ≤ x) , where x is the argument and X is the random variable name. Properties: F(−∞) = 0 F( ) 1 ∞ = 0 ≤ F x( ) ≤ 1 Fb ( ) ≥ Fa ( ), if b>a Continuous random variable Discrete random variable An alternate way to characterize random variables is the probability density function: dF x f x( ) = () dx f x( ) 0, ≥ ∀x x f ( ) x = F(−∞) () + f u du ∫ −∞ x = f u du ( ) ∫ −∞ Page 2 of 7