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Question 1. Single-Unit Auctions ......................................... Within the IPVP, assume N potential risk-neutral bidders and no reserve price. The bidder valuations are independently and identically distributed (iid) with the following cumulative distribution function (cdf): Iii/(vi) = viz; vi E [0,1], 2': 1,2,...,N Assume N = 4 and there is purposeful bidding (no speculative behaviour) and no collusion among bidders. (a) Find the probability density function (pdf) of this distribution. Calculate the mean and variance of the distribution. (b) Explain the equilibrium bidding strategy at an English auction. (c) Solve for the equilibrium bid function at an Dutch or F PSB auction. (d) Solve for the equilibrium bid function at an All-Pay auction. (e) Write a Python code to plot the equilibrium bidding strategies derived in parts EL and@ Explain the intuition behind your answer. (f) Find the probability density function of the winning bid W at an FPSB auction where W equals 0(V1;N)- (g) Calculate the expected revenue under the FPSB auction