The uniform-distribution tag has no wiki summary.
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uniform test for a clustering algorithm
I have some clusters of data. Each cluster contains ablout 5 data points. How can I assign a score to these clusters (a real number) that indicates how uniformly these data points are in clusters. In ...
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1answer
147 views
Probability that two numbers do not follow each other and are distributed over a sequence
Assume a sequence $S$ of numbers out of the set $N={1..n}$.
Example:
$$S = "123312"$$
Set of all pairs would be:
$$M = (2,3),(3,3), (3,1)$$
Not in $M$:
$(1,1)$ : not occuring in the sequence next ...
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2answers
242 views
Calculating probabilities in two overlapping continuous uniform random variables (with an added constraint)
Given X~unif(a, b) and Y~unif(c, d) with a < c < b < d.
What's the probability that Y>X and Y being realized in the interval (c, b)?
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1answer
64 views
Whats the probability that a set of dunif random variables is strictly ordered?
Let $\{X_i\}$ be $n$ iid dunif(0, u) (discrete uniform) random variables with u>n. How do I compute the probability that $\{X_{i+1}\}$ > $\{X_i\}$ for all i?
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1answer
110 views
Very Important question. Limiting distribution
I have an exam in the morning and there is still one question I cannot do.
$X_1, \ldots, X_n$ are iid random variables each having distribution with density $f_{X_i}(x;\theta)= 1/\theta$, for $x ...
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Generating samples from $u(7,10)$
I have the following assignment:
It requires to generate samples from $u(7,10)$,the uniform distribution on the interval $2 \leq x \leq 11$. Compare the normalized histogram with the density ...
3
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1answer
206 views
Average sine of an angle between two rays in a cone
I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle.
Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
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1answer
38 views
Uniform Continuous R.V. - Optimization
working on this problem:
A road construction company needs to decide where to place an
emergency phone on a stretch of road of length L. Suppose that
accidents can happen uniformly at random ...
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1answer
1k views
Continuous Random Variable - Uniform Median, Exponential Mode
Working on this question:
The median of a continuous random variable with CDF $F(x)$ is the
value $m$ that guarantees that
$$P\{X > m\} = P\{X < m\} = \frac{1}{2}$$ The mode
is the ...
1
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1answer
220 views
Normal Random Variable - uniform distribution
So here's the question I'm trying to solve:
A stock price movement model supposes that if the current stock price
is s, then, after one period, the stock price will be $us$ with
probability ...
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1answer
290 views
Uniform Random Quaternion In a restricted angle range
I'm trying to sample uniform random rotations. I'd like the rotations to be restricted in a range [-θ,θ]. I found a method by K. Shoemake which can be summarized as:
...
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Approximation or calculation of the probability of getting “clumps” when sampling from a uniform distribution
Suppose that there are $n$ independent samples $X_1,X_2,...,X_n$ sampled from the uniform distribution on $[0,1]$ with the pdf $f(x)=1$.
Is there a good way to calculate or approximate the ...
3
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1answer
118 views
Estimating number drawn from one distribution based on sum of that number and number drawn from another distribution
I have been working on this for several days and have been unable to come up with an answer. The problem is very simple to state, but it seems difficult to solve.
A computer draws a number $x$ at ...
1
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1answer
215 views
PDF/CDF and expected value of a function
How can I compute the PDF/CDF and expected value of the following function:
$$
\frac{\alpha}{r^2}
$$
where $r$ is generated as follows:
draw $x$ and $y$ from a uniform distribution in the range ...
3
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1answer
277 views
Probability that, given a set of uniform random variables, the difference between the two smallest values is greater than a certain value
Let $\{X_i\}$ be $n$ iid uniform(0, 1) random variables. How do I compute the probability that the difference between the second smallest value and the smallest value is at least $c$?
I've messed ...
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2answers
493 views
Probability of difference of random variables
How can I compute this probability? I do not know what to do since it involves two random variables.
Let $X$ and $Y$ be uniform random variables on $(0,1)$. How can I compute this?
$$
P(|X-Y| < ...
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1answer
182 views
Rank of a random variable that follows a Uniform Distribution (0,1)
Well the question is a little easier .. Let X be a random variable that follows a Uniform distribution (0,1)(Uniform Standard). What is rank of the variable? (Values can take). I have a confusion ...
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2answers
129 views
converting random sequence
There is stream (sequence) of uniform random integers $x_i$, each integer in $[0,N-1]$ range, where N is not power of 2.
I need to convert it to sequence of integers [0..255] (bytes), such that ...
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1answer
209 views
Demonstrations of the expectation and variance of discrete uniform distribution
I'm studying for my exam of probability distributions and in my study book got these equalities:
=
Also mention that: is equal to
how to reach these inequalities?
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1answer
79 views
Probability of uniform distribution
If I have an array of $n$ numbers in the range [0,1) and have the following events for $y$:
for $i=1$ to $n$ :
generate a new number $y$ in [0,1) uniformly and independent of previous
if $y\ge0.5$ ...
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2answers
116 views
Why is $P(X<0)$ the same as $P(X\le 0)$ for continuous distributions?
In uniform distribution, a continuous distribution, for example where $A = -1$ and $B = 1$,
$P(X < 0)$ is said to be the same as $P(X \le 0)$. Why is this?
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1answer
252 views
The “beach problem”: does anyone know it? or know how to solve it?
The following problem was given some years ago in the German computer-science contest for pupils ("Bundeswettbewerb Informatik"). It was originally wrapped in a story which I will briefly translate ...
