Parameter estimation problem: let the population obey the uniform distribution of θ - 1 / 2 to θ + 1 / 2, x1, X2 Xn is the sample from the population, and the sample mean is x average Let the population obey the uniform distribution from θ - 1 / 2 to θ + 1 / 2, x1, X2 Xn is the sample from the population. The mean value of sample X and (x (1) + X (n)) / 2 are unbiased estimates of θ. Which is more effective? The key is how to find the variance of (x (1) + X (n)) / 2. X (1) represents the minimum value of n samples, and X (n) represents the maximum value of n samples

Parameter estimation problem: let the population obey the uniform distribution of θ - 1 / 2 to θ + 1 / 2, x1, X2 Xn is the sample from the population, and the sample mean is x average Let the population obey the uniform distribution from θ - 1 / 2 to θ + 1 / 2, x1, X2 Xn is the sample from the population. The mean value of sample X and (x (1) + X (n)) / 2 are unbiased estimates of θ. Which is more effective? The key is how to find the variance of (x (1) + X (n)) / 2. X (1) represents the minimum value of n samples, and X (n) represents the maximum value of n samples

f_ x(1)(x)=[1-[1-(x-θ+1/2)]^n]/=n(1/2-x+θ)^(n-1),(θ-1/2