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Basic Concepts of Random Samples Fundamental definitions from MCS 142: “A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.” “A probability sample is a sample chosen by chance. We must know what samples are possible and what chance, or probability, each possible sample has.” (Moore & McCabe, Introduction to the Practice of Statistics 4/e, Freeman, New York, 2003, p. 250). The sample space S is our model of the population. THE SPREADSHEET VIEW OF SAMPLES Row Individual X = weight Y = height 1 s1 x1 = X(s1) y1 2 s2 x2 = X(s2) y2 3 s3 x3 = X(s3) y3 n sn xn = X(sn) yn Other r.v.s Notation: The upper-case letters X1, X2, X3, …, Xn denote random variables; Xj denotes a numerical characteristic of the jth individual in the sample. We may view Xj as the “X” characteristic of the jth individual sj : Xj = X(sj). The lower-case letters x1, x2, x3, …, xn denote non-random numerical values of the aforementioned random variables: xj = a numerical value of Xj. An MCS-341, 342 definition: “Suppose that X1, X2, X3, …, Xn is an identically and independently distributed (i.i.d.) sequence, i.e., X1, X2, …, Xn is a sample from some distribution.” (Evans & Rosenthal, p. 199) In effect, the sample space S becomes the set of real numbers, an infinite population, so this model is not suitable for samples from a finite population, unless the population is large.