1
vote
3answers
60 views

Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i) $. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
0
votes
2answers
49 views

Distribute a population size based on fractions using random number generator drand48()

I have a population size of say 5000 people. Every person belongs to either A, B, C or D category. I want to split the population as per a given fraction provided by user. for example, 99% of A, 0.4% ...
2
votes
0answers
65 views

How to construct a uniform joint distribution

I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. ...
1
vote
0answers
34 views

choose a list of words such that have equal letter frequency

I have a big list meaning full Words. surely letter frequency of this word list is different for each letter. Now my problem is to find a way to randomly select words from this word list to a new ...
1
vote
1answer
1k views

Probability density of Continuous uniform distribution over the unit circle

If we want to chose a point $(x,y)$ uniformly at random from a unit circle in a plane, why is the joint probability density of the random variable $f(x,y) = \frac{1}{\pi}$ for $x^2+y^2\leq1$? The ...
0
votes
0answers
36 views

Slicing Up Uniform Random Rotation Quaternions

I'm generating uniform random rotations using quaternions. I am using the method attributed to Shoemake, which is discussed in another post (Uniform Random Quaternion In a restricted angle range): ...
0
votes
1answer
322 views

Uniform distribution of points on the surface of a circle around a randomly chosen point

In a Monte Carlo simulation i have encountered the following problem: given a unity vector u defining a point A on the surface of a unity sphere, i must randomly determine a new vector forming an ...
1
vote
1answer
326 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 ...
0
votes
1answer
714 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: ...
2
votes
2answers
161 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 ...