a)

There are 9 bidders with valuations that are independently and uniformly distributed between 0 and 1. What will Bidder 1 bid if its valuation is 0.5 in the symmetric equilibrium of a second-price auction? Round your answer to two decimal places.

b)There are 3 bidders with valuations that are independently and uniformly distributed between 0 and 1. In equilibrium, what will Bidder 1 bid in a first-price auction if its valuation is 0.1? Round your answer to two decimal places.

c)There are 4 bidders with valuations that are independently and uniformly distributed between 0 and 1. In equilibrium, what is the probability that Bidder 1's bid is less than 0.3 in a first-price auction? Round your answer to two decimal places.

d)There are 4 bidders with valuations that are independently and uniformly distributed between 0 and 1. In equilibrium, what is the probability that the highest bid is less than 0.5 in a first-price auction? Round your answer to two decimal places.