For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.

# Questions tagged [uniform-distribution]

2209 questions

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### Can the sum of two non-degenerative random variables ever be uniform?

Background
A rather famous problem is regarding if the sum of loaded dice can be uniformly distributed over $\{2, \cdots, 12\}$; the answer is no. We can see that the top answer in the above link can be generalized to an $n$-sided dice for odd $n$.…

Tom Chen

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### Expected value of the square of the sum of two uniformly distributed independent random variables

What is $E[(X + Y)^2]$, where $X,Y ~ U(0,1)$ and independent ?
edit: I have tried expanding the brackets which results in the following:
$E[X^2 + 2XY + Y^2]$, can you write this expression as $E[X^2] + 2E[XY] + E[Y^2]$ ?

wimon

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### Variance for area and volume?

A machine manufactures cubes with a side length which varies Uniformly over the interval $[0.2, 0.3]$ in millimeters.
For the following problems, make sure you use the correct units. (Assume the
sides of the base and the height are all the same.)
a.…

user865043

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### What is the probability that the receiver catches the ball?

A quarterback needs to throw the ball quickly,
and in his haste, the location it lands is Uniformly distributed within a $30×120$
sq. ft. area in the endzone. The receiver can only catch the ball the ball lands
within $7$ feet of him, i.e., within a…

user865043

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### Probability of two variables of having the same value

Let $X$ and $Y$ be two random variables, whose PDFs $f_X$ and $f_Y$ are uniform. $f_X$ and $f_Y$ may overlap. For instance, they could represent two score distributions for two tuples $x$ and $y$ in a database.
Which is the probability for $X$ and…

Eleanore

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### You believe that there's a fly somewhere less then 6 feet away from you.

You believe that there is a fly somewhere less than $6$ feet away from you. If you believe that he is located Uniformly in a circle of radius $6$ feet away from you, what is the probability that he is more than $2$ feet away from you?
My work:
This…

user865043

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### Computing the probability that a function of random variables takes particular values

If one rolls two fair die, the sum of the two rolls is most likely to be $7$, and $2$ and $12$ are very improbable. Likewise, if one averages two random numbers in the interval $[0,1]$, the most likely result is $0.5$ and the most unlikely are $0$…

BGreen

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### In this Probability Density Function, am I doing it right?

Consider a model consisting of random variables $X,Y$ and $Z: Y=Xw+Z$, where $Z∼U[−1,1]$.

Fred

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### Computation with a transformation of a random variable.

The random variable $X$ is uniformly distributed on the interval $[-4,4]$. Compute $P(X^2 ≤ 9)$.
I tried to define $Y = X^2$ and compute the density of this transformed variable. The PDF of the uniform distribution is $f_x(x) = \frac{1}{8}$. What I…

Luca

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### Calculate odds some $n$ numbers, picked from the same uniform distribution, occurring within some interval of eachother

Consider three sets of random numbers, $A,B$ and $C$, with known sizes $p,q,r$, picked from the same uniform distribution on $[x,y]$. What is the probability of an $a\in A$, $b\in B$, and $c\in C$ (picked at random) being within some $\Delta$-wide…

10GeV

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### Black Jack Game Probability

I am reviewing for my upcoming test but I have difficulty in solving one problem because the way the define the variable X causing my confusion.I really need your help to build up a good solution for this problem.
Jack plays a game which assigns a…

Hoang Nam

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### Given a random variable whose density is given by a uniform distribution, can we use the expected value to calculate another expected value?

If given a random variable X whose density is given by the following uniform distribution,
$$p(x)= \begin{cases}
1 & \ 0

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### Density Function of Uniform Distribution?

I had this problem from my last question:
Given that:
$X \sim \text{Uni}(a,b)$.
I know that the density function is:
$$f_X(x) = \begin{cases} \dfrac{1}{b-a} &x \in [a,b] \\ 0 & \text{otherwise}. \end{cases}$$
Then How can this help me to find the…

White Force

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### Distribution of concatenating two uniform random numbers

Suppose I have two indepent random number generators $RNG_1$ and $RNG_2$, each output random numbers of range $[0, 2^{31}-1]$ with equal probability. I shall make a new random number generator of uniform distribution $[0, 2^{63}-1]$ by sampling two…

Guibao Wang

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### Coding the uniform probability density function

In the chapter about the probability of Data Science from Scratch the author says:
the density function for the uniform distribution is just:
def uniform_pdf(x):
return 1 if x>= 0 and x <1 else 0
Whereas on Wikipedia, one can read that
The…

Revolucion for Monica

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