All Questions
Tagged with convolution density-function
48
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Preservation of strict log-concavity under convolution
I have spent an embarrassing amount of time trying to prove or disprove any of this. I am aware that a similar question was posted in 2014, but since I couldn't make anything out of the two sources ...
- 13
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61
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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
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1
answer
68
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"Deconvoluting" the sum of independent random variables
I encountered the following question in my research. See here for some background, but this post should be self-contained. Suppose
$X$ follows a discrete uniform distribution on $m$ points $\{X_1, ...
- 836
1
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1
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71
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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
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55
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W.s.s. Gaussian process in LTI, probability of the output signal
Let {${X(t); t\in ℝ}$} be a wide sense stationary Gaussian process with mean $\mu_X = 1$ and power spectral density $$S_X(f) = \begin{cases} 1, \ \text{if} \ |f| < 5; \\ 0, \ \text{otherwise}.
\...
- 93
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1
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255
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Finding distribution and density function of $X^2/(X^2+Y^2)$ where $X,Y∼N(0,1)$
I have two random independent standard normal variables $X,Y∼N(0,1)$.
How can I find the distribution of $\,\dfrac{X^2}{X^2+Y^2}\;?$
I know that if we talk about only $X^2$ then it will be a Chi-...
- 11
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1
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46
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Probability density of $X_1 − 2X_2$, where $X_1, X_2$ independent and exponentially distributed.
Problem
Consider $X_1, X_2 \sim \varepsilon(1)$ independent and define $T = X_1 - 2X_2$.
I want to calculate the probability density function (pdf) of $T$, denoted by $f_T$, which can be obtained by ...
- 151
1
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1
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538
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PDF of $|X-Y|$ when X and Y are independent uniform on $\left[0,l\right]$
pretty much trying to solve the question in the title, what I tried is:
consider $Z=\left|Y-X\right|$, and try to compute $F_{Z}\left(t\right)=1-P\left(Z>t\right)=1-\left(P\left(X-Y>t\right)+P\...
- 121
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78
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How to prove that probability density function of the sum of 2 independant variable is equal to their convolution?
The probability density function of the sum of two independent random variables is the convolution of their individual probability density functions.
What is the simplest demonstration that proves ...
- 139
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2
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98
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Density of $X_1 + X_2$ using convolution
Let $X_1$ and $X_2$ be independent random variables continuously uniformly distributed on $[−1, 1]$ and $[0, 5]$, respectively.
Determine, with intermediate steps, the density of $X_1 + X_2$. To do ...
- 14k
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24
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For any probability density function f, does it always exists another probability g such that f = g∗g? (* means convolution)
I just learned the theory of convolution between functions, for a probability density function, is there always existing another function g such that f = g * g (convolve with itself?)
0
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1
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91
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If $f_{X,Y}(x,y)=4e^{-2(x+y)}$, find the pdf of $X+Y$
I need to find the pdf of $X+Y$.
I tried Jacobian method and Cdf method but two outputs are different.
Can someone plz help me solve this problem? These are my solution process.
jacobian-> $Z=X+Y$ ...
- 29
2
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0
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621
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Convex combination of random variables
Let $X, Y$ two independent real random variables. If I define the distance of the distribution (i.e. the cumulative density function) of $X$ with a target distribution $F$ as
$$\sup_t |F_X(t)-F(t)|$$
...
- 1,199
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2
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315
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Convolution $\arcsin$ pdf's: $\;\displaystyle \int \frac{1}{\pi \sqrt{1-\tau^{2}}} \cdot \frac{1}{\pi \sqrt{1-(R-\tau)^{2}}} \ d \tau$
Regarding topic: SE I encountered a convolution of two identical $\arcsin$ distributions. The probability density function $pdf$ for $R \in [−1,1]$ in this context is:
$$f(R)=\frac{1}{\pi \sqrt{1-R^2}}...
- 708
1
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1
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387
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Convolution of two independent uniform variables
Question: Let's say $X$ and $Y$ are two independent random variables with $Uniform (0,3)$ distribution. What is the probability density function of $X+Y$?
In solution, it is told to use convolution ...
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