Assume that a population of interest has a uniform distribution on the interval [0, θ], where θ is an unknown parameter we wish to estimate. Let {X1, X2, …, XN} be a random sample of data drawn from the population, and define the random variable Y = Max {X1, X2, …, XN}. Y is frequently used as an estimator for θ. Calculate the bias of Y. (Hint: Determine the distribution function of Y, and use this information to calculate the associated density function.) Note: If random variable X has a uniform distribution on the interval [a, b], the density function fX (z) = 1/(b – a) for all z ϵ [a, b]; fX (z) = 0 for all other z.