Curiosity struck me after I did a probability question today. Is the following statement true?
Let
be a random variable with support in 
. 
, the cumulative distribution function of , is strictly increasing in if and only if is a continuous random variable.
It turns out that this ISN'T true, and you actually need that has *absolute continuity*, rather than being strictly increasing.
Discussion can be found here: http://ift.tt/1AHW201 .
Let
be a random variable with support in . , the cumulative distribution function of , is strictly increasing in if and only if is a continuous random variable.It turns out that this ISN'T true, and you actually need that
has *absolute continuity*, rather than being strictly increasing.Discussion can be found here: http://ift.tt/1AHW201 .
Necessary and Sufficient Condition for X to Be a Continuous Random Variable
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