Question

You are given a number of i.i.d. (independent and identically distributed) observations that are (continuously) uniformly distributed in the interval from X to X+9 , where X is an unknown real valued parameter. Derive the ML (maximum likelihood) estimator for X. Given the observations 31.80 , 28.78 , 30.77 , 28.39 , 27.46 , 35.63 , 29.89 , 29.84 , 30.18 , 31.38 , 33.01 , 27.41 , 34.76 , 32.21 , 34.87 , compute the ML estimate for X. If the ML estimate is a range of values, then compute the midpoint of the interval of ML estimates and provide it as your answer. Round your answer to three decimal digits after the decimal point.

Answer 1