Determination of estimators mean variance standard deviation

Determination of estimators, mean, variance, standard deviation and Confidence Intervals.

Solution

Estimators : let us consider a random sample x1, x2, ……xn from a population then the function of the sample observations T₁ =₁(x1, x2, ……xn) , T₂ =₂(x1, x2, ……xn), T₃ =₃(x1, x2, ……xn)……….. T_n =_n(x1, x2, ……xn) such that their distribution is concentrated on the possible values of the parameters. The estimating function are called as estimators. We have four good estimator

Mean : it is determined as sum of the observations divided by the number of observations.

Variance : it is defined as the sum of the squares of the deviations of the given observations.

Standard deviation : it is defined as square root of variance

Confident interval :   let f(x,) be the probability function of the parent population from which the samples are drawn. Let t=t(x1,x2….xn) a function of sample values be an estimator of the population parameter , with a sampling distribution. Let [c1,c2] be the confidence interval with a confidence coefficient (1 – ) then c1,c2 are said to confidence limits