Person A is throwing a ball in a field. The ball lands at a random point between markers A and B. Let L be the random variable for the landing point measured as the distance from B. What would the distribution of L be? and how would we go to write its probability density function.
Stating the distribution and writing the PDF
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1It seems like the only reasonable choice is a [continuous uniform distribution](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)). – 2017-02-27
1 Answers
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The problem omits several pieces of information, so I will supply what I think the poser meant:
First of all, when he says a "random point between $A$ and $B$", that tells me that he means a random point on a line between $A$ and $B$ (even though the problem uses the word "field").
Secondly, when the problem just says random, it likely means random, uniformly distributed on that line."
Under those circumstances, $$ f(L) = \left\{ \begin{array}{ll} \frac{1}{|A-B|} & 0\leq L \leq |A-B|\\ 0 & \mbox{otherwise} \end{array}\right. $$