1 / 7

MULTIPLE CONTINUOUS r.v

MULTIPLE CONTINUOUS r.v. JCFD (joint CDF) for r.v X & Y: F X,Y (x,y) = P[X < x, Y < y] JPDF :. Marginal pdf. X, Y r.v’s with JPDF f X,Y (x,y). the marginal pdf of X is just f X (x) : Similarly for the marginal pdf of Y:. Functions of 2 r.v’s.

rashad-henderson
Download Presentation

MULTIPLE CONTINUOUS r.v

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MULTIPLE CONTINUOUS r.v • JCFD (joint CDF) for r.v X & Y: FX,Y(x,y) = P[X < x, Y < y] • JPDF : Chpt. 5

  2. Marginal pdf • X, Y r.v’s with JPDF fX,Y(x,y). • the marginal pdf of X is just fX(x) : • Similarly for the marginal pdf of Y: Chpt. 5

  3. Functions of 2 r.v’s • 2 r.v’s X, Y with JPDF fX,Y(x,y). We may be interested in some function W=g(X,Y) • To determine the corresponding pdf and cdf of W : fW(w), and FW(w). Chpt. 5

  4. Expectation Values for 2 r.v’s X & Ywith respect to JPDF fX,Y(x,y) • E[W]=E[g(X,Y)] - w.r.t JPDF fX,Y(x,y) • E[X+Y] = E[X] +E[Y] • COVARIANCE • CORRELATION COEFFICIENT Chpt. 5

  5. CONDITIONAL PDF • conditional expectation value of g(X,Y) given y : will use conditional pdf fX|Y(x|y) Chpt. 5

  6. INDEPENDENT R.V’s • X, Y are independent • X, Y indep. then Cov[X,Y] = 0 • E[ g(X). h(Y) ] = E[g(X)] . E[h(Y)] • Var[X+Y] = Var[X] + Var[Y] Chpt. 5

  7. JOINTLY GAUSSIAN R.V’s • Jointly Gaussian : if all the marginal PDF’s of the r.v’s are Gaussian • bivariate Gaussian PDF (2 r.v’s) : • marginal PDF’s fX(x), fY(y) • conditional PDF of Y given X • correlation coefficient rX,Y Chpt. 5

More Related