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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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View Full DocumentSimplifying gives
Question 2 c
Given the RV
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 Fall '08
 Jablonowski

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