# Questions tagged [exponential-distribution]

A distribution describing the time between events in a Poisson process; a continuous analogue of the geometric distribution.

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### Distributive property of probabilistic inequalities involving random variables on both sides

Can I break down $P(h \geq (A + B)$, given all $A,B,h$ are all random variables. Will the following rule works? $$P[h \geq (A + B)] = P(h\geq A) + P(h\geq B)$$ Actually, in one of my mathematical ...
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### Memoryless conditional expectation of shifted function exponential

Related to this, is the following valid: \begin{align} E[f(X-t) \mid X>t] = \int f(y-t) f_{X|X>t}(y) dy = \int f(x) f_{X|X>t}(x+t)dx = \int f(x) f_X(x) dx = E[f(X)] \end{align} where I make ...
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### Log-likelihood of a exponential distribution

I have an exercise that I don't quite understand: The life of 100 lamps has been measured. Each lamp has been used with a intensity between 0 and 1, where 0 is off and 1 is the maximum intensity. It ...
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### Why does the distribution of the exponential random variable change to uniform distribution in this case?

I came across this very interesting question in a forum: If both X and Y are independent and exponentially distributed with parameter $\lambda$, find $E[X^2|X+Y]$ Someone gave the solution and ...
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### What is the PDF describing the minimum distance in time between any event and the remaining N-1 events? (for a “process”-making events at fixed rate)

Previously I asked the following question, which is "What is the PDF for the minimum difference between a random number and a set of random numbers?" I want to translate what I learned from ...
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### Distribution of the median of an exponential distribution?

Say i have $X_{ij} \sim Exp(\theta)$ for $i=1...n,\;\;j=1...k$. Afterwards I derive $k$ medians for $k$ groups of size $n$ (even number). The median is a random variable say $M_j$. Do we have any ...
### Quantile-calculation example: Why the term $c$?
I need help to interpret a solution to the following example: Based on historical claim amounts $x_1,...,x_{47}$, which are assumed to be outcomes from an unknown claim distribution, you are ...