STAT 3201- Midterm Exam Guide - Comprehensive Notes for the exam ( 12 pages long!)
12 Oct 2017
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Central limit theorem: let y1,y2, ,yn be a random sample (independent and identically distributed) of n from a population with mean and variance 2. Note: this is exact if the population has a normal distribution as we saw in last lecture. Example: assume population has a chi-squared distribution, n is the sample size, draw. Allows us to use normal probability calculations to answer questions about sample means from many observations. Says that if a large enough sample is drawn, the sample averages for any random variable will have a normal distribution. Says that if the population distribution is normal then the distribution of the sample mean is also normal irrespective of the sample size. Is a very useful result, and is used extensively in practice. Example: kindergarten children have heights that average 39 inches with a standard deviation of 2 inches. A random sample of 35 children is taken.
