HW1_solee - STAT157HW1Solutions

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http://www.stat.ucla.edu/~dinov/courses_students.dir/10/Spring/Stats157.dir/ 1 STAT 157 HW1 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/10/Spring/Stats157.dir/ Problem 1. 1.a: (6 points) Determine the Relative Frequency and the Cumulative Relative Frequency (fill in the two last columns of the table) Clearness Index Number of Days Relative Freq Cumulative Rel Freq Model Probabilities 0.16 0.20 3 0.008219178 0.008219178 0 0.21 0.25 5 0.01369863 0.021917808 0 0.26 0.30 6 0.016438356 0.038356164 .0005 0.31 0.35 8 0.021917808 0.060273973 .0022 0.36 0.40 12 0.032876712 0.093150685 .0076 0.41 0.45 16 0.043835616 0.136986301 .0233 0.46 0.50 24 0.065753425 0.202739726 .0605 0.51 0.55 39 0.106849315 0.309589041 .1332 0.56 0.60 51 0.139726027 0.449315068 .2367 0.61 0.65 106 0.290410959 0.739726027 .2811 0.66 0.70 84 0.230136986 0.969863014 .2000 0.71 0.75 11 0.030136986 1 .0540 1.b: (6 points) Sketch the Relative Frequency histogram and comment on it The relative frequency histogram is normalized such that the height of each column is equal to the probability that the clearness index falls within the bin of that column. The distribution is left skewed, and unimodal.
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http://www.stat.ucla.edu/~dinov/courses_students.dir/10/Spring/Stats157.dir/ 3 1.c: (6 points) Visually choose a model distribution for these data using SOCR Distributions, compute and enter the corresponding model probabilities for each range in the last column. I visually chose the Weibull distribution with Shape=9 Scale =.63. These parameters matched the data reasonably close, so I did not rescale it. If you used a different distribution and a linear transformation to convert the x axis units, that’s perfectly acceptable. The probabilities for each interval are recorded in the above table using the distribution tool. 1.d: (7 points) Cloudy days are those with the clearness index < 0.35. What proportion of the days were
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HW1_solee - STAT157HW1Solutions

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