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Questions tagged [exponential-distribution]

To be used for questions on using, finding, or otherwise relating to Exponential Distributions.

For an Exponential distribution as a probability density function:

$f(x;\lambda) =\lambda e^{-\lambda x}\quad$ for $x \ge 0 $

and

$f(x;\lambda) =0\quad$ for $x \lt 0 $

where $\lambda$ is the rate parameter.

1492 questions
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Expected estimator with exponential distribution

Given time $t$ in minutes, that is exponentially distributed with density $f(t)=\phi e^{-\phi t}$, $t>0$ and $\phi$ is an unknown parameter. Given $n$ observations $t_1,t_2,...,t_n$ find the probability maximum estimate $\hat \phi$ for the unknown…
Mampenda
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Does exponential distribution assume proportionality?

For example if I'm given $\lambda = 3$ births every $5$ minutes this average rate must be proportional to the length of the period. Correct? So $\lambda = 3/5$ births every minute via proportionality. Correct? This is an assumption we must make to…
user911315
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Find the natural parameter space of an exponential family with $h=e^{-x^2}$

Determine the natural parameter space of the exponential family of distribution of dimension one with $\chi=1, T=x,h=e^{-x^2}$. And $h(x)=e^{-|x|}$. Work: The natural parameter space is the set of $\theta$ such that the integral in…
Vons
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Slightly different memorylessness of exponential distribution

I'm stuck on an exercise, which goes as follows: Let $ X $ be an exponentially distributed random variable. Show that \begin{equation} P(X\leq s+t\mid X>s)=P(X\leq t) \end{equation} for all $ s,t\geq0 $. I know that $ P(X\leq s+t|X>s)=\frac{P((X\leq…
silenceofthreeparts
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Random Variable for which sum is exponentially distributed.

Let $X_1,...,X_k\sim D$ IID. What can we say about distributions $D$ so $\sum_iX_i\sim E(\lambda)$? Do such distributions even exist? What if $X_1,...,X_k$ are not IID?
Alexander Mathiasen
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Continuous random events with exponential time

Suppose $N_t$ = # events in the interval $[0,T]$. The time for each event to occur follows an exponential distribution with parameter $\lambda$ i.e. $E_i \sim \exp(\lambda)$. \begin{align} P(N_t =k) = P(\sum_{i=1}^{k}E_i\leq t, \sum_{i=1}^{k+1}E_i>…
steve mike
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How was this step in integration done?

So there’s a sum, about light bulbs. I have $n$ lightbulbs, and the failure times of each lightbulb follow an exponential distribution with parameter $\theta$. I have to find the expected failure time of the first and last light bulbs. I can see…
AP _
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Calculus Proof of An Example of Exponential Distribution Memoryless Property

$E[X^2|X>1] = E[(X+1)^2]$ By the memoryless property, the conditional distribution of $X$, given that $X>1$, is the same as the unconditional distribution of $X+1$. Therefore, the equation stands. I'm trying to prove $$P(X|X>1) = P(X+1)$$ as given…
underdisplayname
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How to interpret the identity function in this formula?

I am confused by the identity function notation in a formula: $f(y|\theta)= \theta\cdot e^{-\theta\cdot y}I_{(0, \infty)}(y)$ Could someone help me understand what $I_{(0, \infty)}(y)$ means in the formula? Thank you so much in advance!
Chenglu
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conditional probability of expected value for exponential distribution

Let's assume that X is a random variable which follows exponential distribution. The expected value of this distribution is E . How can I compute the following probability: $P(X\leq E)$ Thank you so much
Angelıque
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Can anyone help me with this problem on exponential distribution please?

Ten years ago at a certain insurance company, the size of claims under homeowner insurance policies had an exponential distribution. Furthermore, 25% of claims were less than \$1000. Today, the size of claims still has an exponential distribution…
Y.Knight
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What does the expression 'exponentially distributed fading power' means?

I am trying to understand a research article which states the following, $h_{t,u}^v \sim exp(1)$ denotes the exponentially distributed fading power from transmitter $t$ to the receiver $u$ over Rayleigh fading channel. Can anyone help me to…
SJa
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Exponential Distribution - Who finishes first?

Question: Anne and Betty enter a beauty parlor simultaneously, Anne to get a manicure and Betty to get a haircut. Suppose the time for a manicure (haircut) is exponentially distributed with mean 20 (30) minutes. (a) What is the probability Anne gets…
Lakshay Kharbanda
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Finding an average for a section of an exponential function

So I have this exponential function that I don't really understand: I have never studied anything to do with "r" and am attempting to use this information to find an average mass. I would have used a larger range of planets, but I could not find a…
Alex Robinson
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Time for first disk failure which is exponentially distributed

This is not homework, but exam preparation. Suppose disk $A$ fails in an exponential distribution with parameter $\lambda$ (meaning, in average it fails every $\frac{1}{\lambda}$ time), and disk $B$ fails in an exponential distribution with…
TheNotMe
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