Questions tagged [exponential-distribution]
To be used for questions on using, finding, or otherwise relating to Exponential Distributions.
1,541 questions
3 votes
1 answer
59 views
Conditional probability for linear combinations of independent exponentials
I am working on the following exercise. Let $$X_1 \sim \mathrm{Exp}\left(\tfrac12\right), \qquad X_2 \sim \mathrm{Exp}\left(\tfrac12\right),$$ independent. Define $$Y_1 = X_1 + 2X_2, \qquad Y_2 = 2X_1 ...
- 377
0 votes
0 answers
52 views
Density of the sample range $X_{(n)}-X_{(1)}$ and midrange $\frac{X_{(n)}+X_{(1)}}{2}$ of i.i.d. $\exp(\lambda = 1)$ r.v.
I've been trying to find the densities and expected values of the sample range $X_{(n)}-X_{(1)}$ and midrange $\frac{X_{(n)}+X_{(1)}}{2}$ where $X_{(i)}$ denotes the $i$th order statistic from a ...
1 vote
2 answers
98 views
Doubt in Possion and Exponential Distribution co-relation
I was solving the following problem from debore: At time t = 0, 20 identical components are tested. The lifetime distribution of each is exponential with parameter λ. The experimenter then leaves the ...
0 votes
0 answers
48 views
The power of a test of an exponential distribution
Let $X_1,\dots,X_n$ be a random sample from an exponential distribution with unknown parameter $\theta$. Consider the hypothesis $H_0: \theta=\theta_0$ with alternative $H_a: \theta < \theta_0$, ...
- 6,188
3 votes
2 answers
119 views
Memoryless Property with light bulbs
Studying properties of the exponential distribution I encountered the following problem: $n$ light bulbs of different types are lit simultaneously. The lifetimes of these bulbs are independent random ...
- 915
4 votes
3 answers
251 views
How to dither binned data (following a geometric distribution) to recover the exponential distribution?
Consider a random variable 𝑋 that follows an exponential distribution. After binning (floor), 𝑋 becomes discrete and follows a geometric distribution. My question is: how can we recover the original ...
- 143
0 votes
0 answers
48 views
Why Normal Survival Function decaying slower than the Exponential?
The Normal Survival Function decaying slower than the Exponential on LogLog plot. Why? Isn't it supposed to be other way around, as Normal is super exponential $\sim e^{-t^2}$ and should decay faster ...
- 123
-1 votes
2 answers
92 views
Correct answer of $E(W_4| N(1) = 2)$
I'm studying Poisson process and I have questions about how to calculate the expected arrival times conditional on the number of events. I see this exercise in the book "Introduction to ...
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