Notes from 2/16 and 2/18
Notes from 2/16 and 2/18 ENGR 0020: Probability and statistics for Engineers I
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This 2 page Class Notes was uploaded by Emily Binakonsky on Friday February 20, 2015. The Class Notes belongs to ENGR 0020: Probability and statistics for Engineers I at University of Pittsburgh taught by Maryam Mofrad in Spring2015. Since its upload, it has received 88 views. For similar materials see Probability and Statistics for Engineers 1 in Engineering and Tech at University of Pittsburgh.
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Date Created: 02/20/15
Uniform Distribution Normal Distribution Emily Binakonsky Probability Distribution Probability density function pdf of X is a function fx st for any two numbers a and b px S X S b ff x dx The density curve is the graph of f For fx to be a pdf is must satisfy 0 fx 2 O for all values of x o the area bounded by the graph and the x axis must equal 1 The Uniform Distribution Very simple the density function is considered to be flat X random chosen point on the fixed interval ab The distribution function will be 1 fx m39 a S x S b 0 else where And the mean and standard deviation of the pdf is given by a b 2 b a2 M T 2 a T 12 Normal Distribution MOST important distribution Normal Curve that is symmetric about the mean and bell shaped Different values of a affect the shape of the curve Continuous random variable X is said to have a normal distribution with mean u and standard deviation 0 where the pdf of X is 1 egg 02 xao ooltxltoo f VZHU The mean and standard deviation of the normal distribution are bounded by 00 lt a lt 00 and a gt O Uniform Distribution Normal Distribution Emily Binakonsky IV The standard normal distribution Where u 0 and o 1 is used as a reference distribution to help calculate other normal distribution probabilities The standard normal distribution is tabulated Z is denoted as the standard normal random variable The cdf of Z is PZ S 2 and it is denoted as g0z When using the standard normal curve 0 Finding the probability for a particular value of X x I You must transformstandardize x in the following way 35 l1 a I Then use the standard normal table to calculate the area under the curve aka probability 0 Finding the corresponding value of random variable X for a given probability I Use the standard normal table to find the corresponding 2 value I Then transform 2 to x in the following way x ox M V Exponential Distribution Has parameters 3 the mean which must be greater than Oand o the stand The Probability Distribution function of X is E fx Ee xgt0 whereBgtO 0 otherwise The mean and variance is given by the following it B 02 32 The Memoryless Property of the experimental distribution influences the application types of the exponential distribution in component and reliability The relationship between the poison Process and the Exponential Distribution is as follows 0 Let X be the time to the first Poisson event The probability that the length of time until the first event will exceed x is the same as the probability that no Poisson events will occur in x M gt x mm em 4 1 pOSXSx1 e gtxexpltX Notation st such that
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