# 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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### PDF of Z = XY for Jointly Uniform (X,Y) with Parabolic Region

Suppose that $(X,Y)$ is uniformly distributed on the subset of $\; \mathbb R^2$ defined by the inequalities $0 < X < 1$ and $0 < Y < X^2$. Determine the probability density function ...
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### Density of Uniform distribution with respect to standard-normal distribution

How do I calculate the density function of the uniform distribution $U_{a,b}$ with respect to standard-normal distribution $N(0,1)$?
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### Metric for uniformness of distribution of points in an irregular shape

I am looking for a mathematical way to check if the distribution of points inside some region (almost never a proper form) are evenly and uniformly distributed through it. Do you think this is ...
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### An extended warranty pays a benefit of $100$ if failure occurs between time $t = 1.5$ and $t = 8$. Find $P(w<79)$.

The time until failure, $T$, of a product is modeled by a uniform distribution on $[0, 10]$. An extended warranty pays a benefit of $100$ if failure occurs between time $t = 1.5$ and $t = 8$. The ...
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### A stick is broken and its left part is discarded.Probability that one of them $>1$ [duplicate]

A stick of length $2$ m is made of uniformly dense material. A point is chosen randomly on the stick and the stick is broken at that point. The left portion of the stick is discarded and now again ...
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### Type I and type II errors

Let $X \sim uniform(0,\theta)$ we are testing $H_0: \theta = 1$ vs $H_1: \theta >1$ If we know that we reject $H_0$ if $X>0.9$ (1) find $\alpha$, the type I error (2)Suppose that $\theta=1.1$. ...
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### Uniformly Distributed Random-Variable With Specific Ordering

Let $0\leq a<b$. Define the subset of $[a,b]^n$ by $$X=\{(x_1,\cdots,x_{n-1})\mid b^{2n}\geq x_1^{2(n-1)}\geq\cdots\geq x_{n-1}^2\geq a\}$$ What is the probability that a uniformly distributed ...
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### Uniform distribution over the unit disk

Suppose that $U_1$ and $U_2$ are independent, and identically and uniformly distributed over the unit disk, i.e., for $i = 1,2$, $U_i = (X_i, Y_i)$ and the joint density is f_{(X_i,...
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### Minimal Sufficient Statistic for $U(0, \theta)$

The definition of a Minimal Sufficient Statistic (MSS) denoted $S(X)$ is $$\frac{L(\theta;x)}{L(\theta;x)} \text{ independent of \theta} \iff S(X) = S(Y),$$ assuming the densities exist and $L$ ...
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### Finding CDF and PDF of $Y=20/X$ when $X$ is uniform on $[4,7]$

I have a problem where $X$ is uniform on the interval $[4,7]$ and $Y = 20/X$. I am asked to find $F_Y(y)$ and $f_Y(y)$ using the CDF and PDF. This is a uniform distribution, so it's easy enough ...
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### Uniform Distribution and First-Price Sealed Bid

For the First-Price Sealed Bid, I know that the optimal bid is $$(n-1)/n * v_i$$ However, I am confused about a step in finding this value. We are told that there are $n$ players each with a ...
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### Probability (Uniform Distribution Question)

Question: A large wooden floor is laid with strips 2 inches wide with negligible space between the strips. A uniform circular disk of diameter 2.25 is dropped at random on the floor. What is the ...
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### Geometric probability of intersection of a square and a circle

In the unitary square we choose a point $(X, Y)$ with iid coordinates $U [0,1]$ and a radius $R$, independent of $(X, Y)$ and $U [0,1]$, and we draw the circle of radius $R$ with center $(X, Y)$. Find ...
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### Uniform Distribution: Probability that $X$ is rational

In Rosenthal's A First Look At Rigorous Probability Theory one of the phrases about a random variable $X$ having a Uniform Distribution from $0$ to $1$ is the following: ...But now suppose we ask, ...
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### Finding $P\left(X<\frac{3n}{2}\right)$ where $X$ is uniform on $\{n,n+1,\ldots,2n\}$ [closed]
If $X\sim \text{Uniform}\{n,n+1,\ldots,2n\}$, how can I find $P\left(X<\frac{3n}{2}\right)$ (in terms of $n$ where relevant) for both odd and even values of $n$? I got this in a test today and I ...