ART - Does E-Procurement Save the State Money 2009

The document discusses the probability function and expected value of the first order statistic in an auction where bids are independently drawn. It starts by introducing the probability function of the first order statistic and its relationship with the bids. It then derives the probability function of the first order statistic based on the independently drawn bids. Next, it introduces the variable "s" and defines its relationship with the first order statistic. It calculates the derivative of the probability function with respect to "s" and provides the formula for the expected value of the first order statistic. Finally, it discusses the case where the bids are distributed according to a log-normal distribution and provides the probability density function for this case. It then calculates the expected value of the first order statistic for the log-normal distribution.