# Questions tagged [uniform-distribution]

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

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### can a linear combination of normally distributed random variables be uniformly distributed? [closed]

With X ~ N(2,4), Y ~ N(5,7) and Z ~ N(-3,9) and Cov(X,Z) = -5, Cov(X,Y) = Cov(Y,Z) = 0. Given that 2X-4Y+9Z gets you a mean (-43) and variance (677). Is U[-43, 677] a valid linear combination for X, Y ...
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### Uniform distribution always exists on a closed convex compact set?

Let $X$ be a topological space with a weak order $\succsim$. $C\subset X$ is a closed convex compact set. What additional topological assumptions do we need to ensure that $C$ always has uniform ...
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### Recursive Uniform Distribution Expectation Question

Suppose we draw some k ~ Unif(0, 1). Then, we will draw some $u_1$ ~ Unif(0, 1). If $u_1 < k,$ we stop. Else, we will draw $u_2$ ~ Unif(0, $u_1$). We will continue drawing until $u_n < k.$ What ...
1 vote
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### Expectation of sum of indicator function on uniform random variable

Let C be an estimator defined as $$C = \frac{1}{n}\sum_{k=0}^{n}1_{U_k>a}$$ where $a$ is a real number in $(0,1)$ , $1$ is an indicator function and $U_k$ are uniform random variable in $(0,1)$. I ...
1 vote
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### Conditional distribution of sum of squared iid uniforms

Is it true, that if $U_{1}$ and $U_{2}$ are iid uniform distributed variables on $\left[-1,1\right]$, then the sum of $U_{1}^{2}$ and $U_{2}^{2}$ is still uniform distributed conditioned on the set ...
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### Question regarding bounds for Uniform Joint Distributions

I am doing joint probability and i came across a problem with bounds of the joint probability. Let $X, Y, Z$ be independent and uniformly distributed over $(0, 1)$. Compute $Pr(X ≥ Y Z)$. From the ...
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### Variance of sum of n distinct Uniform Random variables

I came across a problem in Quantguide which read: Suppose you continually randomly sample nested intervals from [0,1], halving the size each time. That is, the next interval is [x,x+0.5], where x∼U(0,...
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### Find the Expected Travel Distance of the Ambulance (Where did I go wrong?)

Problem: The county hospital is located at the center of a square whose sides are 3 miles wide. If an accident occurs within this square, then the hospital sends out an ambulance. The road network is ...
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### Convolution of two uniform probability densities (two square waves)

Assuming $X$ and $Y$ are i.i.d. random variables let $Z = X + Y$ $$f_X(x) = f_Y(y) = \begin{cases} 1/2 & -1 \le x \le 1 \\ 0 & \text{else} \end{cases}$$ Find the density ...
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### Expected value of maximum of two D20 rolls

I'm trying to work through a similar version of this problem. The idea is that you have a fair, 20-sided die, and $n$ turns. You are trying to decide how many times to roll it (each roll costs a turn)...
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### Rosenthal First Look at Rigorous Probability Theory Uniform Construction from Bernoulli

I am reading the mentioned book by Rosenthal, in particular pg 74 where a uniform is constructed from an infinite sum of i.i.d. Bernoulli, i.e., $P(X_i=0)=P(X_i=1)=\frac{1}{2}$ with U=\sum_{k=1}^{\...
PROBLEM: Given that $X$, $Y$ are indepedent uniformly distributed r.vs's over range $[0,1]$ with their joint pdf given by: $f_{X,Y}(x,y)=1$ find $P( \frac{1}{\sqrt{2}}\leq (\frac{X^2}{Y^2})\leq\sqrt{... 0 votes 1 answer 38 views ### Find the CDF of W? need to verify. [closed] My main answer for CDF is root(W)/10. 4 votes 2 answers 153 views ### Expected Value of a DnD/Baldur's Gate Feat The Baldur's gate feat Savage Attacker lets you reroll an attack, and choose the better of the two attacks. I am attempting to calculate the expected benefit of this feat. Assume, for the sake of ... 3 votes 0 answers 162 views ### I need a rigorous explanation of Shoemake method to sample uniformly from the group of unit quaternions I know and understand the subgroup algorithm to sample from uniform distribution on the rotation group$SO\left( 3 \right)$, following the following steps: sample$\theta_{1}$from$\text{Unif}\left[ ...
Suppose I have a uniform distribution $X$ ~ U($0, θ$). I have an estimator which pertains to the random variable of the largest value among my random sample. We can express this as max\$(X_1, X_2...X_n)...