STAB22H3 Lecture Notes - Lecture 17: Central Limit Theorem, Sampling Distribution, Standard Deviation
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STAB22H3 Full Course Notes
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Post-lecture seventeen and eighteen: de nition: a collection of random variables x1, x2, . , xn is called a sample if they are independent and identically distributed: denote by x the sample mean of a sample x1, x2, . , xn having common distribution with mean and standard deviation then x has mean also but standard deviation : proving this is a simple application of our rules for mean and variances. n. Consider the following discrete probability distribution with mean. = 0. 9. n which: i sampled from this distribution 500 times. The rst sample was of size 1 and a sample mean calculated. The second sample was of size 2 and a sample mean calculated. The last sample was of size 500 and a sample mean calculated: the (partial) results are tabled below. Observed values x1 = 1 x1 = 2, x2 = 11 x1 = 1, x2 = 4, x3 = 0.
