HW #3-solution - PGE 337 HW#3 SOLUTION KEY Question 1 a I...

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PGE 337 HW #3 SOLUTION KEY Question 1 a I. II. The median is the 50 th percentile and can be obtained from a plot of the cdf -1 2 We see that the median is in the discontinuity observed in the cdf. Since only two outcomes are possible and there is a jump at -1 directly to 2/3, the median is -1. III. The mode is -1 since it has the highest pdf value IV. Since the mean is different from and less than the mode, then this distribution is asymmetric and skewed to the left. This is also confirmed by the difference between the median and the mean values. Question 1 b Given the RV I. II. Median is 50 th percentile given as the cdf value at X = 0.5 Solving the quadratic gives since III. Mode is the maximum of the pdf i.e. IV. The mean, median and mode are similar hence the distribution can be considered fairly symmetric Question 2 a Given the RV I. Solving the quadratic gives since II. Similarly as above, III. Interquantile range is Question 2 b Given the RV
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Simplifying gives Question 2 c Given the RV Question 3 a
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