All Questions
7 questions
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
-2
votes
2
answers
1k
views
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
0
votes
1
answer
3k
views
Mean and Variance of the Area of a Circle with Uniform Radius
A circle with a random radius R∼Unif(0,1) is generated. Let A be its area.(a) Find the mean and variance of A, without first finding the CDF or PDF of A.(b) Find the CDF and PDF of A.
So, quite ...
2
votes
1
answer
354
views
How to compute the CDF of this random variable?
I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. Specifically, one player has the opportunity to choose any value $\eta$ from ...
- 99
4
votes
2
answers
373
views
What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables
$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs.
...
- 347
49
votes
5
answers
42k
views
Why is the CDF of a sample uniformly distributed
I read here that given a sample $ X_1,X_2,...,X_n $ from a continuous distribution with cdf $ F_X $, the sample corresponding to $ U_i = F_X(X_i) $ follows a standard uniform distribution.
I have ...
- 493
13
votes
1
answer
3k
views
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) ...
- 445