The estimator we will focus on for now is the sample

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Unformatted text preview: estimator we will focus on for now is the sample mean. Under some conditions it is successful to approximate the population mean: n x= ¯ i =1 xi x1 + x2 + · · · + xn = n n Notice how x is a function of the the particular sample values we have. ¯ Utku Suleymanoglu (UMich) Sampling Distributions 3 / 21 Introduction Sampling We want x to be a good guess of the unknown µ. So it is important how the x ’s are ¯ selected. Drawing a sample from a population is called sampling. So what is the best way to sample? A course on its own. We will focus on the basic but most important way. Random Sampling. Simple Random Sample: For finite populations. Each population member has the same probability to be chosen. Random Sample: For infinite populations. Each draw is independent from the others. For most of our purposes we can think of random sampling as randomly picking independent numbers from a population with some distribution (not known) with mean µ and variance σ 2 (neither is known). Utku Suleymanoglu (UMich) Sampling Distributions 4 / 21 Introduction Point Estimation We talked about the population parameters and est...
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