2) X and Y are jointly continuous with joint pdf

From what I gather from your latest comments, the PDF is given to be

and in particular, f(x, y) = cxy over the unit square [0, 1]², meaning for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (As opposed to the unbounded domain, x ≤ 0 *and* y ≤ 1.)

(a) Find c such that f is a proper density function. This would require

(b) Get the marginal density of X by integrating the joint density with respect to y :

(c) Get the marginal density of Y by integrating with respect to x instead:

(d) The conditional distribution of X given Y can obtained by dividing the joint density by the marginal density of Y (which follows directly from the definition of conditional probability):

(e) From the definition of expectation:

(f) Note that the density of X | Y in part (d) identical to the marginal density of X found in (b), so yes, X and Y are indeed independent.

The result in (e) agrees with this conclusion, since E[XY] = E[X] E[Y] (but keep in mind that this is a property of independent random variables; equality alone does not imply independence.)

g

step-by-step explanation:

5050 i think

step-by-step explanation: