Suppose X and Y are independent variables such that X is uniformly distributed i

Question

Suppose X and Y are independent variables such that X is uniformly distributed in the interval [0, 2] and Y is uniformly distributed in the interval [1, 2]. What is the probability that Z = XY <= 1 (where "<=" means less than or equal to)? Hints: Consider the joint distribution of X, Y over a certain rectangle. Determine the set corresponding to XY <= 1 and compute an integral. We know that (X, Y) is uniformly distributed over the rectangle...what are the corners of the rectangle? The value of the joint probability density function f(x,y) on this rectangle is what? What does the region of that rectangle corresponding to xy<=1 look like? What is the probability that (x,y) lands in this region?

Explanation / Answer

If X

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