Lecture5 - Lecture 5: Measures of Center and Variability...

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Lecture 5: Measures of Center and Variability for Distributions (Population); Quartiles, Boxplots for Data (Sample) Chapter 2
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2.1 Measures of Center (Distributions) Mean for continuous distributions Let f(x) be the density function for a continuous random variable X , then the mean of X is: Mean for discrete distributions Let p(x) be the mass function for a continuous random variable X , then the mean of X is: = dx x f x X ) ( μ = ) ( x p x X
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Examples—Means Continuous distributions Normal ( µ , σ ) — µ Exponential ( λ ) 1/ λ Uniform ( a, b ) — ( a+b )/2 Discrete distributions Binomial ( n, π ) — n π Poisson ( λ ) — λ
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Example 1 Find the mean value of a variable x with density function: f(x) = 1.5(1-x^2), 0<x<1 = 0, o.w. What’s the median of X distribution?
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Median for continuous distributions Let f(x) be the density function for a continuous random variable X , then the median of X is whatever value which satisfies: What is the median of a Normal Distribution? If a continuous distribution is perfectly
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Lecture5 - Lecture 5: Measures of Center and Variability...

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