0
votes
1answer
29 views

Exponential Distribution as a density function

I have an important presentation on tuesday about the exponential distribuion as a density function. My question is: What are the advantages of using this function? In order to fulfill my task i have ...
2
votes
2answers
42 views

What's the density of $Z=\max(X,Y)-\min(X,Y)$ with $X,Y$ exponentials of parameter $\lambda$?

Let be $X,Y$ two independent exponential random variables with parameter $\lambda$. What is the pdf of $Z=\max(X,Y)-\min(X,Y)$? Thanks for your help.
1
vote
2answers
38 views

How do I transform an r.v. using the floor function? (exponential distribution)

Just had a bash at this question for my Intro to Maths Stats module...I got to the end with a probability density function rather than a probability mass function, namely $f_Y(y) = \lambda a ...
0
votes
0answers
63 views

Expected waiting time of the process in the queue given that the process is served

Consider the following situation: There is one server with exponential service time with parameter $\lambda$. One process is waiting in the queue. The waiting time is exponential with parameter ...
1
vote
1answer
59 views

Product of exponential distributions

Suppose $X_1$ is $\mathrm{Exp}(\lambda_1)$ and $X_2$ is $\mathrm{Exp}(\lambda_2)$. $X_1$ and $X_2$ are independent. Let $Y = \min (X_1, X_2)$ and $Z = \max (X_1, X_2)$ and $W = ZY$ . Compute the ...
2
votes
1answer
25 views

n events of one process occuring before m events of another process

Assume that you have two independent Poisson processes, N1( t ) with rate λ1 and N2( t ) with rate λ2 . What is the probability that n events occur in the first process before m events occur in the ...
0
votes
1answer
49 views

Naming and meaning of exponential power functions

I apologize if something like this has already been asked, but I don't have any ideas on search terms for this family of functions. I'd like to know two things: 1) Is there a name for the family of ...
0
votes
1answer
89 views

probability of maximum of two independent random variable

Suppose $X$ and $Y$ are two independant random variable with exponential distribution with paramet $\lambda=1$ and $M=$max{$X$,$Y$}. Then $P(M \ge 4)$ is equal to : Answer: 0.036 how do i come to ...
2
votes
1answer
68 views

How to prove that if $\int_t^\infty(s-t-\frac{1}{\lambda})\,f(s)\ ds =0$ for all $t\ge 0$ then $f(s)=\lambda\, \mathrm{e}^{-\lambda s}$

The problem is motivated by my probability text which states that if the expectation of time to wait conditioned on time already spent waiting $(t)$ is constant (equals $\frac{1}{\lambda}$) then the ...
2
votes
1answer
50 views

Median and Mean of Sum of Two Exponentials

I have a cumulative distribution function: $$G(x) = -ae^{-xb} - ce^{-xd}+h$$ The associated probability density function is: $$g(x) = abe^{-xb} + cde^{-xd}$$ My problem concerns $x\ge 0, X \in R$. I ...
1
vote
2answers
156 views

PDF and CDF of the division of two Random variables

I have two RVs; their PDF are as the followings: \begin{split} f_{X}(x) = \frac 1 {a} e^{-\frac x {a}}\end{split} and \begin{split} f_{Y}(y) = \frac {y^{L-1}} {b^{L} \Gamma (L)} e^{-\frac y ...
1
vote
0answers
58 views

Negative exponential/ exponential power distribution between 0 .0 and 1.0?

Note: I'm not very familiar with distribution and higher level math Heyho, I'm currently looking for a way to generate random values between 0.0 and 1.0 with an exponential power or negative ...
1
vote
1answer
25 views

Joint distribution proof

I am trying to study for an exam and I am kind of lost on how my professor came to a particular result on his practice exam. Let $W$ be an exponentially distributed random variable with $\lambda = 2$ ...
0
votes
1answer
31 views

Is the distribution of one exponential will be smaller than a second one Uniform?

I came by an expression which I am not sure I understand. If: $X_1 \sim exp(\lambda)$ $X_2 \sim exp(\lambda)$ Then: $P(X_1<X_2|X_2) \sim Uniform(0,1)$ Where it is not clear to me what ...
1
vote
1answer
102 views

How to vary lambda in exponentially distributed numbers

I am implementing an exponentially distributed random number generator (RNG) based on George Marsaglia's Ziggurat algorithm. I previously used the algorithm to create a normally distributed RNG. By ...
1
vote
1answer
1k views

Derive the PDF of the log-normal distribution?

If $X \sim N(0,1)$ and $Y = e^X$, find the PDF of $Y$ using the two methods: (i) Find the CDF of of $Y$ and then differentiate. Use the notation $\Phi(x)$ and $\phi(x)$ for the CDF and PDF of $X$ ...
1
vote
1answer
223 views

Stuck on solving for x in exponential to find variance

The problem seems simple: Let X be an exponential random variable such that $P(X \le 2) = 2P(X > 4)$. Find the variance of X. Easy, right? $ P(x \le 2) = 1 - e^{-2\lambda} $ and $ P(x > 4) = ...
3
votes
4answers
112 views

$X$ is $\text{Exp}(\lambda)$, $Y$ is $\text{Uniform}(0,X)$. How can I find $\Bbb E[Y]$ and $\text{Var}(Y)$?

$X$ is $\text{Exp}(\lambda)$, $Y$ is $\text{Uniform}(0,X)$. How can I find $\Bbb E[Y]$ and $\text{Var}(Y)$? I did tried to plug it like double integral of $\Bbb E[Y]$ from 0 to X which $f(t)$ is ...
1
vote
0answers
44 views

Determining a probability density function from histogrammed data

Data on a set of dwell times has been taken and the histogram of which has been fitted with the function: $$Ae^\frac {-t}{\tau_1} + Be^\frac {-t}{\tau_2}$$ where A is positive and B is negative. ...
1
vote
1answer
322 views

Exponential Probability Monte Carlo simulation

I need to write a Matlab program to estimate the quantity $\theta = \mathrm{Pr}(X < 1)$, where $X$ is an exponential random variable with mean $1$. I am doing this for multiple monte carlo ...
-2
votes
2answers
1k views

How to calculate MEAN of exponential distribution?

$ f(x) = \begin{cases} \frac15 e^{(-\frac15x)}, x>0 \\ 0, \text{elsewhere}\\ \end{cases}$ How to calculate $E[(X+5)]$ and $E[(X+5)^2]$ ? Thanks a lot.
0
votes
1answer
625 views

X1 X2 independent variables exponential distribution - Looking for simpler solution

Let $X_1 \sim \exp(\lambda)$ and $X_2 \sim \exp(\lambda)$ be two independent exponentially distributed random variables. Find the mean and variance of random variable $Y=X_1 + X_2$. $x=x_1 + ...
5
votes
4answers
5k views

Difference between power law distribution and exponential decay

This is probably a silly one, I've read in Wikipedia about power law and exponential decay. I really don't see any difference between them. For example, if I have a histogram or a plot that looks like ...