All Questions
Tagged with convolution random-variables
101
questions
0
votes
1
answer
74
views
Seeking Algorithm to Solve a Convolution Integral or Directly Convolve Two CDFs
Hi everyone,
I'm working on a project where I need to find a way to directly convolve two cumulative distribution functions (CDFs) given in polynomial form, and solve the following convolution ...
- 19
0
votes
0
answers
59
views
Is the convolution between two CDF always well defined?
Given the integral convolution:
$$(F_X * G_X)(x)=\int_{-\infty}^x F_X(t)G_X(x-t)dt $$
and also that the CDF of random variables are bounded between the interval $(0,1)$ and the flipping of one of them ...
- 495
0
votes
0
answers
35
views
Dependent random variables whose convolution adds up
I want to find two dependent random variables $X$ and $Y$ with values in $\mathbb{Z}$ such that $P_X\star P_Y=P_{X+Y}$, where $\star$ is the convolution.
What I've tried:
I was "tickling" ...
- 1,279
0
votes
0
answers
61
views
Probability density function of three independent random variables
I will try to describe the question first and how i solve the problem.
Here we have three independent random variable $X,Y,Z$ and $S_3=X+Y+Z$,
the probability density function of three variable are ...
- 1
1
vote
1
answer
71
views
How does this density function make sense?
Let $X$ be an exponentially distributed random variable with parameter $\beta>0$ and let $Y$ be a random variable with $P(Y=0)=1-p$ and $P(Y=1)=p$, where $0<p<1$. Assume that $X$ and $Y$ are ...
- 59
1
vote
0
answers
46
views
Sum of two random variables (General Formula)
Rather than attempt to derive a general expression for the
distribution of $X + Y$ in the discrete case, we shall consider some
examples. (Ross, A First Course in Probability, Section 6.3.4)
The ...
- 1,834
0
votes
1
answer
100
views
Convolution of two exponential functions where x > 0
Assuming $X$ and $Y$ are i.i.d. random variables let $Z = X + Y$
$$
f_X(x) =
\begin{cases}
\lambda e^{- \lambda x} & x \gt 0 \\
0 & \text{else}
\end{cases}
$$
$$
f_Y(y) =
\...
- 53
2
votes
2
answers
141
views
Convolution of two uniform probability densities (two square waves)
Assuming $X$ and $Y$ are i.i.d. random variables let $Z = X + Y$
$$
f_X(x) = f_Y(y) =
\begin{cases}
1/2 & -1 \le x \le 1 \\
0 & \text{else}
\end{cases}
$$
Find the density ...
- 53
0
votes
0
answers
62
views
Conditions for independence of sum of i.i.d. random variables from remaining
Previously I asked the following question, that does not generally hold:
The following question is very similar to this reference.
Let $(X_{1},X_{2},X_{3})$ be a random vector with continuous ...
- 35
1
vote
2
answers
82
views
Why does the convolution of two probability density functions not work as expected?
I have two independent random variables, $X \sim exp(\lambda)$ and $Y \sim unif(-1,0)$.
I would like to compute the density function $f_Z(z) = \int_{-\infty}^{\infty} f_Y(y) f_X(z-y) dy$, where $Z = X ...
- 25
0
votes
1
answer
80
views
Does KL divergence keep order under convolution? [closed]
Suppose there are three random variables $X,Y,Z$ such that $$D_{KL}(X,Y)\leqslant D_{KL}(X,Z)$$ And there is an independent (with respect to $X,Y,Z$) Gaussian noise $\xi\sim N(0,1)$. Can we say the ...
- 23
1
vote
1
answer
93
views
Computing the sum of two i.i.d uniform random variables inside a unit disk?
I'm trying to find the sum of two independent variables $A$ and $B$ whose densities are defined as follows:
$$f_A(x,y)=\frac{1}{\pi}, \sqrt{x^2+y^2}\le1$$
and
$$f_B(x,y)=\frac{1}{\pi}, \sqrt{x^2+y^2}\...
- 19
0
votes
2
answers
131
views
How to compute the PDF of $Z=XY$
After the answer I got, I'm interested in the case for computing the PDF of a random variable $Z=XY$, and $X, Y$ are independent. The convolution of PDF describe the PDF of the sum of two random ...
- 495
0
votes
1
answer
89
views
What is the correct way of compute PDF of $Y=2X$
Let $X$ be a random variable and $X\sim U(0,1)$. Define a new random variable $Y=2X$, What is the PDF of $Y$, $f_Y(y)$?
If $f_Y(y)$ is calculated as the convolution of the PDF of $X$, $f_X(x)$ with ...
- 495
4
votes
1
answer
391
views
How do I find the probability distributions for multiple dice rolls for dice with a differing number of sides?
I have been learning how to play Dungeons and Dragons recently, and have bought my first set of dice.
The standard DnD dice are:
1d4
1d6
1d8
1d10
1d10 × 10 [10, 20, 30... 90, 100]
1d12
1d20
I was ...
- 163