Linked Questions
19 questions linked to/from Distribution of ratio between two independent uniform random variables
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Ratio of Two Uniform Random Variables [duplicate]
If X1 X2 are independent Uniform variates on (0,1), Find the distribution of Z=X1/X2.
I tried using the CDF method where P(X1<=zX2) is equal to z/2 when z is in(0,1). However, I am unable to find ...
user284824
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Simple function of two random variables, $Z = \frac{Y}{X}$ where Y, X~U(0,1) and independent [duplicate]
I must have missed something important in the formulation of the problem. Can you please help clarify how should the following simple problem be formulated and where my mistake is.
Let $Z = \frac{Y}{X}...
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Why is there -1 in beta distribution density function?
Beta distribution appears under two parametrizations (or here)
$$ f(x) \propto x^{\alpha} (1-x)^{\beta} \tag{1} $$
or the one that seems to be used more commonly
$$ f(x) \propto x^{\alpha-1} (1-x)^{...
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Expected Value of Gamma Distribution
If $X \sim \text{Gamma}(\alpha,\beta)$, how would I go about finding $E\left(\frac 1{X^2}\right)$?
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Distribution of a ratio of uniforms: What is wrong?
Suppose that $X$ and $Y$ are two i.i.d. uniform random variables on the interval $[0,1]$
Let $Z=X/Y$, I am finding the cdf of $Z$, i.e. $ \Pr(Z\leq z) $.
Now, I came up with two ways of doing this. ...
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Proving transformations of two independent chi-squared random variables is equivalent to a Beta distribution
I came across the following in some old class notes of mine:
if $\chi_{v_{1}}^{2}$ is independent of $\chi_{v_{2}}^{2}$ then
$\frac{\chi_{v_{1}}^{2}}{\chi_{v_{1}}^{2}+\chi_{v_{2}}^{2}}\backsim
...
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Is there an estimator for the symmetry of a bimodal distribution?
I would like to know how I can measure the degree of symmetry of a bimodal distribution.
Is there any a criterion like, for example skewness, in the case of unimodal distributions?
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2
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Symmetric distribution with finite Mean but no Variance
Is there a symmetric continuous distribution that has a finite mean, but no variance?
What I've found so far: For instance the Pareto distribution satisfies everything but the symmetry, so I was ...
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6
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1
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Exponentially decaying integral of a Poisson process
Suppose that $X_t$ is the set of times of the events of a Poisson process with unit rate after $t$ seconds. (In other words, $X_t$ is a set of $N$ uniformly distributed points over $[0,t]$ where $N$ ...
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Prove that $P(X \le a) + P\{Y \le \frac{1}{a}\} = 1$
Prove that if $X$ has the F-distribution with $(m, n)$ d.f. and $Y$ has the
F-distribution with $(n, m)$ d.f., then for every $a > 0$,
$$
P(X \le a) + P\left\{Y \le \frac{1}{a}\right\} = 1
$$
I ...
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3
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Symmetry of a ratio of two random variables
My question is whether the fact that two random variables, X and Y, are symmetrically distributed implies that their ratio, Z=X/Y, is symmetrically distributed too.
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2
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Distribution of $X$ conditional on $Z=Y/X,$ when $(X,Y)\stackrel{\text{iid}}{\sim} U(0,1)$
The question I have is:
Define $X,Y$ to be two independent uniform(0,1) random variables and $Z:=\frac{Y}{X}$
Compute $P(X<x|\sigma(Z))$.
The answer given apparently by "straightforward ...
5
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1
answer
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What can we say about distributions of random variables $X$ such that $X$ and its inverse $1/X$ have the same distribution?
What can we say about random variables such that it and its inverse have the same distribution? One example is Cauchy distributed random variables, easily proved via the fact that if $X, Y$ are IID ...
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Conditional probability density of the ratio of two independent uniform random variables with different supports
Let $X = B * [(u + \epsilon_u) - C]$.
$u$ represents a true measurement value.
$\epsilon_u \sim U(-0.5, 0.5)$ represents the error associated with that measurement value.
$u + \epsilon_u > 0$.
$B$ ...
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How to proper evaluate the PDF of a Beta Distribution?
On page 40 of "Think Bayes - Bayesian Statistics Made Simple", Allen evaluates the PDF of the Beta distribution as
...
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