All Questions
14 questions
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156
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Convolution: PDF of difference of uniform random variables [closed]
PDF of $X$:
PDF of $Y$:
$Z=X-Y$, $T=X+2Y$, how to find the PDF of $Z$ and $T$ and plot them?
- 191
1
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1
answer
1k
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Density of square root of sum of squared independent uniform random variables [duplicate]
Let $X \sim U(-1, 1)$ and $X \sim U(-1,1)$. We want to find density function of $W = \sqrt{X^2 + Y^2}$.
I got stuck and I have no idea, where I am making a mistake. This is my approach.
Let $F$ be a ...
- 325
1
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1
answer
803
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Why does Uniform distribution make sense?
This might be a dumb question, but I am suddenly confused on how to understand the PDF of a uniform distribution.
For instance, the PDF of standard uniform is always equal to 1... How is that ...
- 13
5
votes
2
answers
2k
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If $X=\sin\Theta$ and $Y=\cos\Theta$ with $\Theta$ uniformly distributed, how can I compute the joint pdf of $(X,Y)$?
I have a random variable $\Theta$ uniformly distributed between $[-\pi ,\pi]$, two functions $X=\sin\Theta$ and $Y=\cos\Theta$. I know that $X$ and $Y$ are uncorrelated but not independent. I want to ...
- 83
3
votes
1
answer
1k
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Sum of exponential of uniform random variables?
Let $F_{i}$ and $\phi_{i}$ are uniformly distributed independent random variables in the range $[-50,50]$ and $[-\pi/4,\pi/4]$, respectively.
If $N = 10$ and
$$Z = \sum_{i=0}^N e^{j(F_{i}+\phi_{i})}...
- 121
2
votes
1
answer
579
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How to estimate the PDF of the logarithm of a uniformly distributed random variable?
This is a question I have to solve and need help with. I know it's usual to give pointers and hints so the OP can follow from there. Thus, I'll appreciate all input that shows me the way to go.
Let $...
- 706
2
votes
2
answers
411
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What is the ratio of a N[0,1] and U[-1/2,1/2]?
I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
- 13.3k
-2
votes
2
answers
1k
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Uniform Density Function
As we know the uniform probability density function is
f(x)=1/(b-a)
if i find the density function and area of this uniform distribution between
(0, 1/2) then it would be
f(x)=1/(1/2-0)
f(x)=2
...
- 85
1
vote
1
answer
69
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Discrete Distribution
In the die-coin experiment, a fair, standard die is rolled and then a fair coin is tossed the number of times showing on the die. Let N denote the die score and Y the number of heads.
a)I want to ...
- 1,226
8
votes
2
answers
811
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PDF of a sum of dependent variables
This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
- 1,264
17
votes
2
answers
689
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What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?
I have four independent uniformly distributed variables $a,b,c,d$, each in
$[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be $$f_2(u_2)=-\...
- 1,264
1
vote
1
answer
1k
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How do I compute the density of this data set that is made up of two different 3D-distributions?
A sequel to this question.
I have a dataset where:
$\frac{4}{5}$ of the points are drawn from: $(x, y) \sim \mathcal{U}_{2}(0,30)$, $(z) \sim \mathcal{U}_{1}(14.5, 15.5)$.
$\frac{1}{5}$ of the ...
- 165
3
votes
1
answer
413
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Scale parameter MLE scheme known but how to find according distribution PDF?
For known location, we can find the scale parameter of a normal distribution by calculating the sum of squared differences to the location, then dividing by n-1 and taking the square root. This is the ...
- 445
13
votes
1
answer
3k
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Can we make the Irwin-Hall distribution more general?
I need to find a symmetric low-kurtosis distribution class, which includes the uniform, the triangular and the normal Gaussian distribution. The Irwin-Hall distribution (sum of standard uniform) ...
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