Could you please answer this question by providing step by step solution? I would be appreciated! Thanks.

Question 5 [14 points] Consider a first price auction with two buyers 1,2. Their valuations v1, V2 are independent and each follows the triangle distribution in the interval [0, 2], as shown below. Diagram 1 f(x) Vi O 2 (a) [3 points] For any x between 0 and 2, determine the expression of the density function f (x) of the triangle distribution given above. (b) [3 points] For any x between 0 and 2, determine the expression of the distribution function F(x) of the triangle distribution given above.(c) [4 points] The bid functions of buyers 1,2 are bl = km, b2 = km where k1, k2 are positive numbers. Showing all steps of your work, show that the expected net income of buyer 1 is 3 171 @1612 (1 k1) (d) [4 points] Using the arithmetic mean-geometric mean (AM-GM) inequality, determine the choice of [:1 that maximizes the expected net income of buyer 1