Reference no: EM132381295
CIV3204 - Engineering Investigation Assignment Questions, 2019 SEMESTER 2, Monash University, Australia
The assignment for this subject consists of the analysis of stream flow and rainfall data for the Woori Yallock catchment in Victoria. The coordinates of the outlet for this catchment are:
Latitude: -37.76
Longitude: 145.51
Figure 2.1 (attached) shows the outline of the catchment. In the first part of the assignment, the required data need to be downloaded and processed. The second part of the assignment consists of fitting a probability distribution. In the third part, the sampling distribution will be fitted, and some inferences regarding the properties of the data will be made. The fourth and last part will focus on an analysis of a number of linear regressions of the data.
For each part of the assignment, your report should outline how you performed the calculations, and the steps you took to come to your conclusions.
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Table 2.1: List of years to analyze for Assignments 1 and 2 depending on the student ID number.
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Last digit student ID number
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First five years
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Second five years
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Third five years
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0
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1969-1973
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1988-1992
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2005-2009
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1
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1970-1974
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1989-1993
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2006-2010
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2
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1971-1975
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1990-1994
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2007-2011
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3
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1972-1976
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1991-1995
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2008-2012
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4
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1973-1977
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1992-1996
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2009-2013
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5
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1974-1978
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1993-1997
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2010-2014
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6
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1975-1979
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1994-1998
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2011-2015
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7
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1976-1980
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1995-1999
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2012-2016
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8
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1977-1981
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1996-2000
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2013-2017
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9
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1978-1982
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1997-2001
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2014-2018
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2.1 Data Analysis -
Download the stream flow data for the test site.
Download as many years as possible.
Download the daily rainfall data for the nearest rainfall station with a sufficiently long time series, which is Coranderrk Badger Weir. Again, download as many years as possible.
We will work with full years of data, thus from 1969 through 2018.
Important: For this part of the assignment, as well as for part 2, we will work with the logarithms of the nonzero flows.
First, use three sets of five consecutive years (for example 1976 through 1980), making sure the three sets do not overlap. Table 2.1 lists the years to analyze depending on your student ID number. These sets of years are roughly covering the beginning, middle, and end of the time series, respectively. Calculate the mean, standard deviation, and skewness for the stream flow each of the three sets. Calculate the same statistics for one year in each of the three sets. Comparing the one year to the five year statistics, are there any conclusions you can draw?
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Table 2.2: Year to perform a Gaussian probability plot for, depending on the student id number.
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Last digit student id number
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Year to analyze
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0
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2009
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1
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2010
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2
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2011
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3
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2012
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4
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2013
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5
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2014
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6
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2015
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7
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2016
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8
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2017
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9
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2018
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2.2 Probability and Distribution Fitting
For the same data sets as in the first part of the assignment, we will check whether or not the stream flow data follow a lognormal distribution (in other words, if the logarithms of the data follow a Gaussian distribution). We will apply a χ2 test for this purpose, with 5% significance. What conclusions can you draw from this analysis?
We will also test the Gaussianity of the logarithms of the flows through a Gaussian probability plot, as explained in slides 29 and 30 in week 4. Table 2.2 shows the year that you must analyze, depending on your student id number. What do you conclude from this analysis?
Through a routine water quality analysis, it is found that somebody has illegally dumped paint in the river. This paint has been found downstream of an area with50houses.Thismeansthatany of these 50 houses could have polluted the water. Through analyzing the houses, a consultant has determined that there is an 90% chance that the paint used by household A is the paint that is found in the water. Does this mean that there is an 90% chance that household A is guilty of polluting the stream? If yes, explain your reasoning. If not, calculate the chance that the household is guilty, and explain your reasoning.
The council decides to perform a water quality check every day. This test costs $500 each day. If a pollutant is found in the water, they assume that they will find the pollutor, and they will fine them $50,000. What does the probability to find a pollutant in the sample each day at least have to be, for the council to be 90% sure that they will not lose money on these tests, in a non-leap year?
The council is contemplating organizing nature walks along the river with a paid guide. The walks last for a day, and the guide charges $50 per customer per day. The salary of the guide is $1100 per week, and he is expected to guide at least 25 people per week. How certain can the council be that they will be cash-flow positive any random week?
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Table 2.3: List of years to analyze for Assignment 3 depending on the student ID number. L2D stands for the last two digits of your student ID number.
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L2D
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Year
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L2D
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Year
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L2D
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Year
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L2D
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Year
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L2D
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Year
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00
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1969
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01
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1970
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02
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1971
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03
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1972
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04
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1973
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05
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1974
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06
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1975
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07
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1976
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08
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1977
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09
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1978
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10
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1979
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11
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1980
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12
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1981
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13
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1982
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14
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1983
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15
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1784
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16
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1985
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17
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1986
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18
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1987
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19
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1988
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20
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1789
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21
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1990
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22
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1991
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23
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1992
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24
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1993
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25
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1994
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26
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1995
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27
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1996
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28
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1997
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29
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1998
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30
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1999
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31
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2000
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32
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2001
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33
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2002
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34
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2003
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35
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2004
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36
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2005
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37
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2006
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38
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2007
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39
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2008
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40
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2009
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41
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2010
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42
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2011
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43
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2012
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44
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2013
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45
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2014
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46
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2015
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47
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2016
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48
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2017
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49
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2018
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50
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1969
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51
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1970
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52
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1971
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53
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1972
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54
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1973
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55
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1974
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56
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1975
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57
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1976
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58
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1977
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59
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1978
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60
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1979
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61
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1980
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62
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1981
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63
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1982
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64
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1983
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65
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1784
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66
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1985
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67
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1986
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68
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1987
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69
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1988
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70
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1789
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71
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1990
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72
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1991
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73
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1992
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74
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1993
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|
75
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1994
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76
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1995
|
77
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1996
|
78
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1997
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79
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1998
|
|
80
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1999
|
81
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2000
|
82
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2001
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83
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2002
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84
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2003
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85
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2004
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86
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2005
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87
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2006
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88
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2007
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89
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2008
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90
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2009
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91
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2010
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92
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2011
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93
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2012
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94
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2013
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|
95
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2014
|
96
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2015
|
97
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2016
|
98
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2017
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99
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2018
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2.3 - Sampling Distributions
Important: From here on, we work with the raw observations, thus no longer with the logarithms of the nonzero flows.
Table 2.3 lists the year to analyze depending on your student ID number. From the data in that year, take a sample of 100 random discharge observations (with replacement) and calculate the mean. Repeat this 100 times. Plot the distribution of these sample means, and compare to the theoretical sampling distribution. Do the same exercise with 200 and 1000 repetitions. What can you conclude about the obtained distributions?
Assume you have one day with 24 observations. What is the probability that the daily average is going to be larger than 0.5, 1, 2 and 3 m3s-1?
We want to check whether or not the annual averaged stream flow has changed over the years. We will use an ANOVA for this purpose. We will work with annual averages of the stream flow data. The years 1970-1979 are assumed treatment 1, the years 1980-1989 treatment 2, the years 1990-1999 treatment 3, and the years 2000-2009 treatment 4. Check at the 5 and 10% significance levels if the averages for the four decades are different or not. If there are differences, use the Tukey-Kramer procedure to check which decades are different from each other.
We also want to test whether the variability of the time series has changed over the years. Pick a random year in the first five years of the time series, and another in the last five years of the time series. Check if there is a difference at the 5% significance level. Does this change at the 1% significance level?
Note - Section 2.3 is required to be completed. It is statistics regarding ANOVA.
Attachment:- Engineering Investigation Assignment File.rar