# 1. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and varia...

1. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and variance σχ2. Assume that n 2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes x] and x2. Let estimate f x of true mean ux be μΧ-(X1 + x2)/2. Then the random variable associated with estimate Axis estimator Ax- (XI + X2)/2. a. Show the mathematical derivation of the bias (to measure its accuracy) of above estimator i x b. Find the mean square error, MSE, of above estimator u x by using the results of part a and the fact that the standard deviation (to measure its precision) of the above estimator is SD(AX)-ơX/20.5

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