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Stat400Lec10(Ch3.4,3.7) - Stat 400 Lecture 10 Spring 2012...

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Stat 400 Lecture 10 Spring 2012 Review (3.3) Continuous random variable and its c.d.f. Probability density function (p.d.f.), its properties. Mean, variance, moment generating function Percentiles for p.d.f. Comparison between discrete and continuous random variables Today’s Lecture (3.4,3.7) Uniform distribution, its mean, variance, m.g.f. Exponential distribution and its mean, variance. Memoryless properties of exponential distribution. Cauchy distribution, GOT A MOMENT? 1 of 9
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Stat 400 Lecture 10 Spring 2012 Uniform distribution X has a uniform distribution on the interval [ a, b ] if X is equally likely to fall anywhere in the interval [ a, b ] . We write X U ( a, b ) . The p.d.f of X is f X ( x ) = 1 b - a if a x b 0 otherwise Distribution function F X ( x ) : F X ( x ) = 0 , if x < a, x - a b - a , if a x b, 1 , if x > b. Plot of f X ( x ) and F X ( x ) : 2 of 9
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Stat 400 Lecture 10 Spring 2012 Mean, variance and m.g.f. of uniform distribution If X
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