Please answer step by step. thank you. Explain all details and write the coding part. All parts is from same.question so all of them need to be answered. Last part (5d), code please.

Let X and Y have joint density given by f ( x, y ) = xe * - x y , x > 0 , y > 0 otherwise In Parts a** and **b, do not use calculus to integrate. Instead, you should recognize integrals of the well-known density functions, or expectations, or moment generating functions, possibly with some normalizing constants missing, and use only those facts to evaluate the integrals. Highly recommended: In each integral, identify what is constant, what is the variable, and whether you need any normalizing constants. a) Find the density of X, and explain which probability integral facts you used in your calculation. Recognize it as one of the famous ones and state its name and parameters. b) Find the density of Y, and explain which probability integral facts you used in your calculation. c) For x > 0, find the conditional density of Y given X = x. If it is one of the famous ones, identify the family and parameters. d) Find P(Y > - X) by integrating f appropriately, in the order y first, then x. Use probability integral facts wherever possible; also, the derivation of the moment generating function of the standard normal might be helpful. Then use the code cell below to find the numerical value of the chance