A quantity x has cumulative distribution function p(x) = x − x2/4 for 0 ≤ x ≤ 2 and p(x) = 0 for x < 0 and p(x) = 1 for x >
; 2. find the mean and median of x.
1 answer:
Recall that the PDF is given by the derivative of the CDF:
The mean is given by
The median is the number
such that
. We have
but both roots can't be medians. As a matter of fact, the median must satisfy
, so we take the solution with the negative root. So
is the median.
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-Maddison <3
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