# Tagged Questions

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### Computing an expectation with a uniform probability distribution.

Suppose $F$ is a cumulative density function of a uniform distribution between $a=0$ and $b=B$ and $c$ is a positive real number. I need to evaluate the integral $$\int_c^Bq\;\mathrm dF$$ where the ...
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### Expected Value - Uniform distribution over infinite interval

Question: The probability that an error is introduced into a packet is $\alpha$. Messages, consisting of one or more packets, are received at a node. Given that a message has been received free of ...
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### Probability with multiple uniform distributions

Question: Two sources output a number at equal rates. The output from source A is uniformly distributed between 100 and 199, and the output from source B is uniformly distributed between 50 and 249. ...
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### Conditional uniform distribution

I had this question in a quiz, and now that I am reviewing it, I am not sure if why my TA gave me the marks because I am pretty sure I am wrong. Let the r.v. $Y$ follow uniform distribution $U(1,2)$ ...
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### Weak convergence and limiting distribution

I have $X_{i} \sim \operatorname{Unif}\left(0,1\right)$ iid random variables and have to show that $$\frac{4\sum_{i=1}^n iX_{i} - n^2}{n^{3/2}}$$ converges weakly and compute its limit. How can I do ...
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### Find $P(x_2/x_3 \leq a)$ where $x_1,x_2,…,x_n$ - iid ${Uniform}(0,1)$

$x_1,x_2,...,x_n$ - iid ${Uniform}(0,1)$ How to find $$P(x_2/x_3 \leq a)$$ ??? Can I consider $$x_2, x_3$$ as two random variables or do I need to do something special? my attempt is below ...
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### What is the difference between these two questions?

Consider two independent random variables: X~U(0,1) and Y~U(0,2). Let Z = min(X,Y). b) Find F$_Z$(z) in terms of F$_X$(.) and F$_Y$(.). c) Eliminate F$_X$(.) and F$_Y$(.) to find F$_Z$(z). What is ...
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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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### 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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### median of a uniform distribution [0,1]

I need to find the distribution of the median from the given distribution, where n is known to be odd. The formula given in class for this is: $n=2m+1$ where $m\in\mathbb{N}$ ...
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### Prove there exists no uniform distribution on a countable and infinite set.

Can anyone help me with this problem, I can't figure out how to solve it... Let $X$ be a random variable which can take an infinite and countable set of values. Prove that $X$ cannot be ...
### Generating samples from $u(7,10)$
I have the following assignment: It requires to generate samples from $u(7,10)$,the uniform distribution on the interval $2 \leq x \leq 11$. Compare the normalized histogram with the density ...
How can I compute this probability? I do not know what to do since it involves two random variables. Let $X$ and $Y$ be uniform random variables on $(0,1)$. How can I compute this?  P(|X-Y| < ...