Statistics Assignment Help With Joint Probability Law

3.5 Joint Probability Law:

Two random variables X and Y are said to be jointly distributed if they are defined on the same probability space. The sample points consist of 2 tuples. If the joint probability function is denoted by PXY(x,y) then the probability of a certain event E is given by

PXY(x,y) = P[(X,Y) Є E]

(X,Y) is said to belong to E, if in the 2 dimensional space the 2 tuples lie in the borel set B, representing the event E.

3.5.1 Joint probability mass function and marginal and conditional probability function:

Let X and Y be random variables on a sample space S with respective image sets X(S) = { x1, x2,……. xn} and Y(S) ={ y1, y2,……. Ym}. We make the product set

X(S) *Y(S) = { x1, x2,……. xn}*={ y1, y2,……. Ym}

Into a probability space by defining the probability of the ordered pair (xi, yj). the function p on X(S) *Y(S) defined by

Is called the joint probability function of X and Y and is usually represented in the form of the following table:

Two random variables X and Y are said to be independent if

Otherwise they are said to be independent.

Email Based Homework Help in Joint Probability Law

To Schedule a Joint Probability Law tutoring session Live chat
To submit Joint Probability Law assignment click here.

Following are some of the topics in Random Variable And Distribution Function in which we provide help: