CEIE 340 Lecture 2 Statistics and Hydrology

CEIE 340 Lecture 2 Statistics and Hydrology - Watershed...

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1 Water Resource Engineering CEIE 340 Sayedul H. Choudhury, Ph.D. Watershed Characteristics Today’s Topics s Statistical Terminology s Probability s Random Variables s Probability of Discrete and Continuous Random Variables s Moments of a Sample or Distribution Function s Mean s Variance and standard deviation s Skewness s Distribution Function s Binomial Distribution s Normal Distribution s Regression Analysis
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2 Why Use Statistics in Hydrology? s Randomness in data s Weather data s Precipitation s Streamflow s Establish design criteria Applications s Hydrologic and hydraulic design s Storm s Flooding s Dam failure s Drought
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3 Probability s The likelihood of an event where, n = the number of observations on the random variable x that result in outcome x 0 N = the total number of observations on x s An event is defined as the occurrence of a specified value of the random variable (e.g. probability of rain tomorrow). N n ) x p(x = = 0 Probability Example s The height of the coffer dam depends on the level of flooding that can be expected during the period of construction. s 10 years of annual peak flow (largest flow in each year) data are available s Assume, we can allow only a 10% chance that the flood level will exceed the height of the cofferdam during the 1-yr construction period, i.e. p(x=x 0 ) = 0.10 s Therefore, set the height of the cofferdam between the largest and the second largest floods
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4 Random Variables s Two types of random variables – discrete and continuous random variables s Need to distinguish because the computation of probabilities is different for the two types s Discrete random variable is one that only takes distinct values (yes/no, integer, etc), e.g. the outcome of a roll of die may only take a value between 1 and 6. s
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This note was uploaded on 11/11/2009 for the course CEIE 340 taught by Professor Choudhury during the Spring '09 term at George Mason.

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CEIE 340 Lecture 2 Statistics and Hydrology - Watershed...

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