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Lecture3_Part1 - Normal Distribution SUNY at Albany...

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Unformatted text preview: Normal Distribution SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions Normal Distribution X f(x) μ 2 2 2 1 exp 2 1 ) ( x x x x x f PDF: 1. Normal Distribution A. • X : a continuous random variable and -∞ < X < +∞ • ~ : “distributed as” • N : “the normal distribution” • μ x : population mean • σ x 2 : population variance • μ x and σ x 2 are parameters of the distribution. SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions 2 , ~ x x N X SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions Normal Distributions 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 X f(x) μ = 6 μ = 5 SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions SUNY at Albany - Department of Economics Eco 320 Economic Statistics • Distributions Normal Distributions 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 X f(x) σ 2 = 0.0625 σ 2 = 1 2. Properties of Normal Distribution A. The normal distribution is bell-shaped and symmetrical around the mean μ (skewness is 0). B. The mean μ is where the peak of the density occurs, and the standard deviation σ indicates the spread or the girth of the bell curve. These two parameter fully describe a normal distribution....
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