Please walk me through your steps for this problem.

Q3 Conditional Carbohydrates 6 Points Your startup (Silicon Valley Spaghetti) is pioneering a new process for making pasta. A piece starts in machine A with probability 1/2 and in machine B with probability 1/2. The initial length of the piece is a random variable _X. If the piece starts in machine A. X has a uniform distribution on |0, 1]. If the piece starts in machine B. X has a uniform distribution on [0, 2] The piece then enters the stretching machine, resulting in final length Y, which is uniformly distributed on [X, X + 1]. Q3.1 Graphing 3 Points Draw two sketches: 1. A graph of the joint distribution of X and Y, conditional on machine A being selected. 2. A graph of the joint distribution of X and Y, conditional on machine B being selected. You do not need to draw 3-dimensional plots. It is sufficient to draw the support of each joint distribution in the X-Y plane. Q3.2 Which Machine? 3 Points If the piece has final length less than 1, what is the conditional probability that it came from machine A