Mathematics Stack Exchange
Mathematics Stack Exchange

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
5
votes
2 answers

What do we mean by rate in the exponential distribution?

When we talk about $X$ being a RV with an exponential distribution $$f(x)= 1-e^{-\theta x} \,\,\,\,\, \text{for}\,\,\,\ \theta>0$$ we say that it describes the time between two events in a Poisson Process, where $\theta$ is the rate. Does $X$…
Euler_Salter
  • 5,153
2
votes
1 answer

maximum likelihood for the exponential distribution

I found this question on a past exam and i wanted to know if my solution is correct! I apologize if it's not 100% clear but i'm translating it from italian and it's already written in a really bad form to begin with. Let's suppose that 10 rats are…
Alardor
  • 21
1
vote
0 answers

Type I Error Rate Higher than Significance Level in Likelihood Ratio Test for Exponential Distribution

Type I Error Rate Higher than Significance Level in Likelihood Ratio Test for Exponential Distribution Problem Description I am conducting a Likelihood Ratio Test (LRT) to determine if data from a two-parameter exponential distribution fits a…
BINGXIN YAN
  • 11
  • 2
1
vote
0 answers

Ratio between sum of i.i.d. exponential random variables

Let $X_1, . . . , X_n$ be independent random variables from an exponential distribution with rate 1, $Y_i =\sum^{i}_{j=1} X_j$, and $Z_i = \frac{Y_i}{Y_{i+1}}$, $i = 1,\dotsc ,n − 1$, $Z_n = Y_n$. I want to show that the random variables…
WinnieXi
  • 91
1
vote
1 answer

Waiting Time - Exponential distribution

Question: I go to a grocery store and when I check out, there is one line with one customer waiting to be served while the other line has two customers. Naturally I choose to stand in the line with one customer. It seems as though many times the…
cr7
  • 43
1
vote
1 answer

Exponential distribution for continous rv

The time one has to wait $T$ (in hours) between the telephone calls one recieves is random with function $f(t) = (3/2)e^{-\frac{3}{2}t}$ for $t>=0$. Find the expected time between recieved calls and find the corresponding variance. For two…
Mampenda
  • 409
1
vote
1 answer

Difference of two exponential distribution

Let $X\sim Exp(\lambda_1)$ and $Y\sim Exp(\lambda_2)$, with $Z = X - Y$. I am trying to find the pdf of Z, i.e. $f_Z(z)$. Here is what I have got: \begin{align*} f_Z(z) &= \int_0^{z}f_X(z+y)f_Y(y)dy\\ &= \int_0^{z}\lambda_1…
VincentN
  • 97
1
vote
1 answer

Exponential distribution of decay

A container contains 13 particles, at time $t = 0$. The particles decay independently of each other and the time (unit: minutes) for a given particle's decay is a exponentially distributed random variable with expectation value $36.4$. Let $T$…
Kristoffer Jerzy Linder
  • 81
1
vote
1 answer

Evaluating the tail of a distribution

I have data which is exponentially distributed, but my $x$-values are cut off at 500, so there is no tail, and I want to visualise how that tail would look like. How can I do this?
O.Poklev
  • 11
1
vote
1 answer

Does the truncated exponential distribution preserves the memoryless property?

The right truncated exponential distribution would be defined as $$ f(x=t \mid x
Francisco
  • 415
1
vote
2 answers

Exponential Distribution conditional probability $P(Xx)$

So i know that the exponential Distribution is memoryless so $P(X>x+t\mid X>x)=P(X>t)$. However, when we have $P(Xx)$ we cannot apply this right? So we have to use that definition of the conditional to get $\frac{P(xx)}$. For…
Sorfosh
  • 3,266
1
vote
2 answers

Help with adding and subtracting exponents -

I have a problem in my mathematics (as math usually goes...) and it goes like this: $Simplify.$ $(x^4-2x^2y-7)+(7x^4+6xy-3)$ So, I reordered the equation for simplicity's sake. $x^4+7x^4-2x^2y+6xy-7-3$ Then, obvously, I simplified the equation and…
Carlos Carlsen
  • 787
0
votes
2 answers

Second moment bounded for sub-exponential rv

Using the definition that X is a sub-exponential rv if $E(e^{sX})\le \exp({s^2v^2/2})\ \forall s:|s|\le 1/b$ for some $b,v>0$, and the assumption that $E(X^2)<\infty$ ,I need show 2 things: $E(X)=0$ and $E(X^2)
Qwerty
  • 6,165
0
votes
1 answer

How to understand/use exponentially distributed random numbers

I want to emulate a road traffic situation, which should obey the "poisson distribution", and the probability of vehicles entering the road in the "next" time slot being exponentially distributed. My method is to use the following formula: $$ P(X…
xrfang
  • 101
1
2 3