Need help with the proofs below. Thanks!

Proof Practice 2. (12 points total) Broken Rulers You have a ruler of length 2 and you choose a place to break it using a uniform probability distribution. Let random variable X represent the length of the left piece of the ruler. X is distributed uniformly in [i], 2]. You take the left piece of the ruler and once again choose a place to break it using a uniform probability distribution. Let random variable Y be the length of the left piece from the second break. a. [3 points) Draw a picture of the region in the XY plane for which the joint density of X and Y is nonzero. b. {3 points} Compute the joint densityr function for X and Y. {As always, make sure you write a complete expression.) c. (3 points) Compute the marginal probability density for Y, fyfy}. d. {3 points} Compute the conditional probability density of X, conditional on Y = y, fx|y{a|y}. {Make sure you state the values of y for which this exists.)