All Questions
Tagged with expected-value uniform-distribution
45
questions
3
votes
1
answer
275
views
Probability algorithm on strings
Let $x$ be any binary string $\in (0,1)^*.$
The majority language is given by:
$$\text{MAJ}:=\{x\in (0,1)^*:\sum_{i=1}^ {|x|}x_i>\frac{|x|}{2}\},\text{where $x_i$ is the $i$-th position value(...
- 69
5
votes
1
answer
114
views
Need help in calculating $\mathbb{E}(\frac{1}{x_{(2)}-x_{(1)}}\int_{x_{(1)}}^{x_{(2)}} f(t) \ dt)$, where $x_{(i)}$ are related Beta distribution
Suppose $Y, Z \stackrel{\text{iid}}{\sim}\mathrm{Uniform}(0,1)$.
Let $a = g(\min(y,z)),\ b=g(\max(y,z)).$
How can I calculate the expectation $$\mathbb{E}\left[\frac{1}{b-a}\int_a^b f(t) \ dt\right]$$ ...
- 171
0
votes
1
answer
37
views
What is the bias of uniform distribution parameter estimator?
I have a question regarding question 2 of chapter 6 of "All of Statistics" book by Larry Wasserman.
let: $$X_1, ... , X_n \sim \operatorname{Uniform}(0, \theta )$$
and let:
$$\hat{\theta} = \...
1
vote
0
answers
57
views
Joint density of two functions of a uniformly distributed random variable
I'd like to work out $\operatorname{Cov}(\cos(2U), \cos(3U))$ where $U$ is uniformly distributed on $[0, \pi]$.
I believe this involves computing $\mathbb{E}[\cos(2U)\cos(3U)]$. If so, then I first ...
- 345
1
vote
1
answer
62
views
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 $u_n < k,$ where ...
2
votes
1
answer
209
views
In statistics how does one find the mean of a function w.r.t the uniform probability measure?
I am unfamiliar in statistics. My knowledge is in pure mathematics.
Suppose $n\in\mathbb{N}$, where $X$ is in the $\sigma$-algebra of Caratheodory-measurable sets such that $X\subseteq\mathbb{R}^{n}$ ...
- 161
3
votes
1
answer
58
views
Expected Number of Good Pairs
This is a question I had in my interview: we have $N$ i.i.d Uniform$(0, 1)$ random variables. Define a good neighbor for $x_i$ as the point that is closest to $x_i$ in absolute value. We call a pair $...
- 407
1
vote
1
answer
164
views
Expected number after n rounds of uniform~[0,1] draws
If we have a series of $n$ IID random variable $X_i$ that are uniform [0,1], and at each round $i$ we decide to either keep $X_i$ or discard it for the next number. What is our strategy to maximize ...
- 321
3
votes
1
answer
711
views
Expectation for the MLE for a Uniform Discrete Random Variable
$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$
Problem Statement: Suppose that $n$ integers are drawn at random and with replacement from the integers $1,2,\dots,N....
- 5,942
2
votes
0
answers
233
views
Posterior distribution of two i.i.d. uniform r.v. given their difference with graphical intuition
I have two i.i.d. random variables, $\theta_1$ and $\theta_2$ which are uniformly distributed on the unit square. I need to compute the joint posterior distribution of these two variables, given their ...
- 31
1
vote
1
answer
40
views
Where is the error?
I am trying to compute expectation of $X\mathbb I_{[X+Y\le a]}$ where $a$ is a fixed positive integer, $X$ is discrete uniform random variable taking values from $1$ to $a$, and $Y$ another random ...
- 545
3
votes
0
answers
36
views
Expectation of uniform variates
Let $X_{1},X_{2},X_{3}$ be random variates from $U(0,1)$. It is required to compute $E(\frac{X_{1}+X_{2}}{X_{1}+X_{2} + X_{3}})$.
Here is what I did..
$E(\frac{X_{1}+X_{2}}{X_{1}+X_{2} + X_{3}}) = E(1 ...
- 1,048
0
votes
0
answers
365
views
Mean of uniform two-dimensional probability density function
I am trying to calculate the mean of a two-dimensional probability density function, which looks like:
and is defined by
I know that I can calculate this by
However, this is where I get stuck, as I ...
- 101
7
votes
1
answer
112
views
Evaluating (Uniform) Expectations over Non-simple Region
Background. Let $V = (X,Y)$ be a random vector in 2-dimensions uniformly distributed over two disjoint regions $R_X \cup R_Y$ defined as follows:
$$
\begin{align}
R_X &= ([0,1] \times [0,1]) \...
- 384
3
votes
2
answers
1k
views
Expected number of uniform draws to exceed a first uniform draw
I came across the following problem (Problem number 27 from here): Aaron samples from the Uniform(0,1) distribution. Then Brooke repeatedly samples from
the same distribution until she obtains a ...
- 1,202