118 . Suppose that (X,Y) is the outcome of an experiment that must occur in a particular region S in the xj plane. In this context, the region S is called the sample space of the experiment and X and Y are random variables. If D is a region included in S, then the probability of (X, Y) being in D is defined as P[(X,Y) e D] = || P(x, y)dx dy, where p(x, y) is the joint probability density of the experiment. Here, D p(x, y) is a nonnegative function for which p(x, y)dx dy = 1. Assume that a point (X, Y) is chosen arbitrarily in the square [0, 3] × [0, 3] with the probability density Si (x, y) E [0, 3] × [0, 3], p(x, y) = 0 otherwise. Find the probability that the point (X, Y) is inside the unit square and interpret the result.

Let (S, P) be the sample space with S = (1, 2, 3, ..., 10) and P (a) = 1/10 for all a ES. For this sample space, define the random variables X and Y by #2. X(s) = 25 and Y(s) = s a. Evaluate P (X< 10). b. Evaluate P (Y < 10).

Only parts D and E please.

Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.8, Pr(B) = 0.6, Pr(C) = 0.15. 1. Find Pr(A'), Pr(B'), and Pr(C'). Pr(A') = Pr(B') = Pr(C') = 2. If Pr(A U B) = 0.85., find Pr(AN B). Pr(AN B) = 3. Suppose that we know that B and C are disjoint events. Find Pr[BUC. Pr[BUC] = 4. Suppose that instead of being disjoint C C B. Find Pr[B U C]. Pr[BUC] =

A sample space has 3 outcomes, {O1, O2, O3}. Suppose E= {O1, O2}, and F= {O1, O3}. If Pr[E]= 0.67 and Pr[F]= 0.54, what is Pr[{O2, O3}]?