Lesson14_S1.pptx - TAIBAH UNIVERSITY Faculty of...

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TAIBAH UNIVERSITY Faculty of Science Department of Math . ةبيط ةعماج مولعلا ةيلك تايضايرلا مسق Probability and Statistics for Engineers STAT 305 Teacher : Dr.Moustapha Abdellahi First Semester 1438/1439
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Some Continuous Probability Distributions Lesson 14
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Contents 3 Continuous Uniform dist. Normal Distribution
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The probability density function of the continuous uniform random variable X on the interval [A, B] is given by: Continuous Uniform distribution We write X~Uniform( A , B ). elsewhere B x A A B B A x f x f ; 0 ; 1 ) , ; ( ) (
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Continuous Uniform distribution
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Continuous Uniform distribution The density function for a random variable on the interval [1,3].
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The mean and the variance of the continuous uniform distribution on the interval [ A , B ] are: Continuous Uniform distribution Theorem 1: 12 ) ( 2 2 A B 2 B A
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Example : Suppose that, for a certain company, the conference time, X, has a uniform distribution on the interval [0,4] (hours). (a) What is the probability density function of X? (b)What is the probability that any conference lasts at least 3
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Example 1 : (continued) Solution elsewhere x x f x f a ; 0 4 0 ; 4 1 ) 4 , 0 ; ( ) ( ) ( 4 3 4 3 4 1 4 1 ) ( ) 3 ( ) ( dx dx x f X p b
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The graph of the probability density function (pdf) of a normal distribution, called the normal curve, is a bell-shaped curve. Normal distribution
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If the random variable X has a normal distribution with mean and variance 2 , we write: X ~ Normal( , ) or X ~ N( , ) The pdf of X ~ Normal( , ) is given by: Normal distribution 71828 . 2 , 14159 . 3 0 ; 2 1 ) , ; ( ) ( 2 2 1
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