BCOR 2200 Statistics Review

BCOR 2200 Statistics Review - BCOR 2200 Fall 2008...

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BCOR 2200 Fall 2008 David M. Gross Ph. D. Statistics and Normal Distribution Review A way to estimate future events is to examine past events and assume that the pattern will be repeated in the future. We can use this technique to estimate possible ranges in annual returns for investment classes. The first step is to collect a sample of returns over a large number of years, then calculate the mean and standard deviation of the sample of returns. The mean and standard deviation of the actual population are estimated using the sample. Mean = μ X = (X 1 + X 1 + … + X N ) / N Standard Dev. = σ ≈ S X ={[(X 1 X ) 2 + (X 2 X ) 2 + … + (X N X ) 2 ] / (N-1)} 1/2 Note: Divide by N-1 to calculate the standard deviation since we are using a "sample" of past interest rate changes and not ALL past interest rate changes, in which case we would divide by N. Dividing by N-1 produces a larger standard deviation. When we use S X to estimate probable future interest rate changes, we will get a larger estimate. Other Statistics: Median = value which divides the sample. There are just as many observations greater than the median as less than the median Mode = value with the most observations. For reasons of calculation simplicity, we will assume that interest rate changes are NORMALLY distributed. This means that the frequency and probability of observations can be described by what is often called the "bell shaped” curve. One of the reasons for making this "Normality assumption” is that we know certain things about the area under the Normal curve, and can therefore make statistical inferences by assuming normality. Even if the sample of observations is not normally distributed, the population of observations is assumed to be normally distributed. The normal distribution is a type of Probability Density Function (PDF). A PDF is essentially a frequency bar chart (or histogram) with a "line" over the top instead of bars. The shape of the line is described by a function with two parameters (or variables): the mean ( μ ), which gives the center point, and the standard deviation (
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This note was uploaded on 03/17/2009 for the course BCOR 2200 taught by Professor Tomnelson during the Fall '08 term at Colorado.

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BCOR 2200 Statistics Review - BCOR 2200 Fall 2008...

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