Q3: An random experiment consists of marking a point randomly inside a half-circle with a radius of 1, as shown below. Let's call this point N. Let X and Y be the random variables that denote the coordinates such that X is the horizontal coordinate and Y is the vertical coordinate. Answer the following questions. 1 Y A -1 X I The location of N is uniform inside the half-circle, find the joint probability density function of X and Y. Please provide the solution step by step. Find the marginal probability density functions of X and Y. Please provide the solution step by step. (You must also write the range of the random variables!) Let g(X, Y) be the area inside a circle that has the point N as its center and touches the half-circle at a single point, as shown below, in gray. Please note that the small circle can extend beyond the half circle on the bottom. Write g(X, Y) and specify its range. Please provide the solution step by step.

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