# 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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### Expected Value Problem (Q-function…inside a function)

I'm working through my textbook for a communications course I'm taking, and this problem is confusing me big time. Like always, the math questions give me the most problems. Maybe I should take the ...
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### Limit of sum of (continuous) uniform distributions

In my stats courses at university, I've been working on transformations of distributions etcetera. However, one particular case has intrigued me for a while: the sum of continuous uniform ...
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### how to calculate probability?

I'm facing difficulty in understanding how they in the book, jumped for (12.13) to (12.14). what is given is that $b_1$ and $V_2$ are uniformly distributed between $[0,1]$. I could not post a picture ...
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### Rao-Blackwell Uniform Distribution

I am having a bit of an argument with my study group about a Rao-Blackwell problem that we have for our statistical theory class. The problem goes like this: Let X~U(0,$\theta$), and suppose we have ...
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### Uniform Distribution: finding the probability between two variables

Q: In a uniform density $\mathcal{U}(a,b)$ with $a=-0.025$ and $b=0.025$, what is the probability that an error will be between 0.010 and 0.015? A: From the density function, I didn't know how $d$ ...
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### Uniform Probability Distribution

I have a machine part that have lifetime uniformly distributed between 0 years and 1 year. Whenever a part fails, it is immediately replaced with a new identical part. I know that lifetimes of ...
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### Expectation of the min of two independent random variables?

How do you compute the minimum of two independent random variables in the general case ? In the particular case there would be two uniform variables with a difference support, how should one proceed ?...
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### How to estimate parameters of a uniform distribution?

I have information of the order in which students were classified in regard to their scores in a SAT test. I know the distribution of scores for each student is uniform with support [a,b]. I also know ...
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### Uniform distribution, Expected value and standard deviation for proportion of observations in a subintervall

$X\sim U(0,1)$. Divide the interval [0,1] into k equal subintervals. Then $X_1$=the number of observtions on the first interval. Define the new variable $Y_1=X_1/n$, where n is the number of ...
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### Binomial distribution with random parameter uniformly distributed

I have a problem with the following exercise from Geoffrey G. Grimmett, David R. Stirzaker, Probability and Random Processes, Oxford University Press 2001 (page 155, ex. 6): Let $X$ have the ...
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### Uniform distribution

$X~U(0,1)$ Find $E[\sqrt {X}]$ and the probability density function of $Y$ defined as $Y=X^2$. I know that $E[Y]=E[g(X)] = \int_a^b g(x)f(x) dx$ I don't know why this question does not meet the ...
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### Finding Limits of Integration

I have two functions, one depending on $x$ which is $\frac {1} {2} {\delta(x-5)} + \frac {1} {4}$ which is the combination of a dirac delta function at $5$ and a uniform distribution from $5$ to $7$. ...
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### Expected number of overlaps between intervals

Suppose $N$ intervals of length $\delta$ are positioned in $[0,1]$. The starting point $l_i$ of each interval is drawn from an uniform distribution, i.e., $l_i \in [0, 1-\delta]$, thus it will ...
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### equivalence between uniform and normal distribution

The principle of insufficient reason says that all outcomes are equiprobable when we have no knowledge to guess otherwise. I understand this and that this corresponds to uniform distribution. However, ...
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### Distribution of binary digits in moduli

Considering the (infinite) set of all positive integers that are a product of $2$ primes only, represented in binary $100...01$. Question: is the distribution of the proportion of $0,1$ digits "...
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### Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$

Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$