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How to combine two integrals containing the PDFs of a variable and its linear transform?
Original Post:
Suppose we have two random variables $X$ and $Y$ with cumulative distribution functions $F(x)$ and $G(y)$. We know that $Y = aX + b$.
I want to compute $Z(x) = F(x) - G(y)$.
What I have ...
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6
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2
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What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?
Overall question: Assume X$_i$ ~ i.i.d. Unif(0,1). What is the expected length of a sequence that is monotonically increasing when drawn from the distribution?
The skeleton of the solution is
$$
\...
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4
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3
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pdf of $Z_{(n)}/Z_{(1)}$, where $Z \sim \text{Exponential}(1)$, i.i.d. (order statistics)
Let $Z_i \sim \text{Exponential}(1)$, iid, $i=1,2, ..., n$ and let $Z_{(i)}$ be the $i^{\text{th}}$ order statistic.
How can I find the pdf of $T=Z_{(n)}/Z_{(1)}$?
(the ratio of maximum and minimum ...
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