0
votes
1answer
21 views

Let X be a random variable with PDF fx. Find the PDF of the random variable |X| in the following

Here's my question: X is uniformly distributed in the interval $[-1,2]$. Find pdf of $|X|$... So I did P($|X| \le x$) = P($-x \le X \le x$)... From here I'm not too sure how to proceed. I know the ...
2
votes
2answers
40 views

Density of sum of two uniform random variables

I have two uniform random varibles. $X$ is uniform over $[\frac{1}{2},1]$ and $Y$ is uniform over $[0,1]$. I want to find the density funciton for $Z=X+Y$. There are many solutions to this on this ...
1
vote
2answers
48 views

Approximate distribution for the sample mean?

A random variable $X$ is said to follow a discrete uniform distribution if its probability function is given by $$p_X(x) = \left\{ \begin{array}{ll}\frac{1}{\theta}, & x = 1, 2, \ldots, ...
1
vote
0answers
19 views

Injective uniform distribution on an n-sphere

I just asked this question on the stats stackexchange, but I thought that maybe someone on math knew the answer. So: For an application I'm working on, I need to go from some uniformly distributed ...
4
votes
3answers
50 views

Joint density problem. Two uniform distributions

This is the problem: An insurer estimates that Smith's time until death is uniformly distributed on the interval [0,5], and Jone's time until death also uniformly distributed on the interval [0,10]. ...
1
vote
1answer
36 views

Proving that a moment generating function converges pointwise

I have found a moment generating function $M_n$ given by $\cfrac{(1-e^t)e^{\frac tn}}{n(1-e^{\frac tn})}$ if $t\ne 0$ and 1 if $t =0$ How do I prove that $M_n$ converges point-wise to the moment ...
1
vote
1answer
18 views

MLE for lower bound of Uniform Distribution

Let $X_1$, $X_2$, . . . , $X_n$ be a random sample from a $Uniform(θ, 1)$ population, where $θ < 1$. (a) Find the MLE $\widehat{\theta}$ of $θ$. (b) Find constants c and d (possibly depending on ...
1
vote
2answers
33 views

Standard Uniform Distribution

I am trying to show that a random variable $X_2$ has a standard uniform distribution. I have: $\alpha \subset(0,1), X_1 \sim U[0,1],$ and $X_2 = \begin{cases} X_1 &\mbox{if } X_1< \alpha ...
1
vote
1answer
66 views

Power Function for the uniform distribution

Completely stuck on this homework question, I think my knowledge of the power function is nowhere near good enough coming up to finals! Consider the following alternative testing problem: the two ...
8
votes
3answers
209 views

distribution of $X^2 + Y^2$

Suppose $X$ and $Y$ are independent uniform distributions between $(0,1)$. What is the distribution of $X^2 + Y^2$? I derived that the pdf of $X^2$ is $\frac{1}{2\sqrt{x}}$ for $0\leq x \leq 1$. How ...
1
vote
2answers
78 views
0
votes
2answers
58 views

Distribution of ratio of uniform and exponential random variables

This is a homework question, I feel like I'm doing it right, but I can't seem to get the answer to match up. I have a uniform RV from 2 to 4, and an exponential with mean 4, so $X \sim ...
4
votes
1answer
36 views

If $X$ ~$Uni(-1,1)$ show that $X$ and $X^2$ are not independent

I provide my approach in solving this but I amd not entirely sure whether I am correct. Since X~uni(-1,1) $f_X(x)=1/2$ and $F_X(x)=(x+1)/2$. $F_{X^2}(x)$=$Pr[X^2≤x]$=$2F_X(√x)$=$(√x+1)/2$. Hence ...
1
vote
2answers
60 views

Proving Unbiased estimators

Hello all, Here is a question I am struggling to understand, ...
0
votes
0answers
48 views

sum of two independent uniform random variables question

Let ܶ$T_1$ and ܶ$T_2$ be random times for a company to complete two consecutive steps in a certain process. $T_1$ and ܶ$T_2$ are measured in days and their joint probability density function is ...
0
votes
2answers
42 views

Finding the probability density function $Y=|X|$

Suppose $X$ is a uniform $([-1,2])$ random variable. How can I find the probability density function $Y=|X|$?
0
votes
1answer
93 views

Complete Statistic: Uniform distribution

Take a random sample $X_1, X_2,\ldots X_n$ from the distribution $f(x;\theta)=1/\theta$ for $0\le x\le \theta$. I need to show that $Y=\max(X_1,X_2,...,X_n)$ is complete. Now, I know I should ...
3
votes
1answer
24 views

CDF on Standard uniform gives the same distribution

Assume that $X$ has a continuous and strictly increasing CDF $F_X$. Define $Y = F_X^{-1}(U)$ where $U$ is standard Uniform. How dow I show that $X$ and $Y$ have the same distribution?
2
votes
1answer
64 views

What's the distribution of the exponential of uniformly distributed variable?

I want to know the distribution of $z = \exp(j\varphi)$, with $\varphi \sim \mathcal{U}[-\pi;+\pi]$. From the book "Probability, Random Variables and Stochastic Processes" by Papoulis and Pillai I ...
2
votes
1answer
259 views

Show that the nth order statistic is a consistent estimator of a uniform parameter

We assume that our observations come from a uniform $(0,\theta)$ distribution. Can you please check my work on the following? We can derive the distribution function of the maximum of the sample, ...
0
votes
1answer
191 views

Sufficient statistic for uniform distribution

Given random sample $\left\{ { X }_{ 1 },{ X }_{ 2 },...,{ X }_{ n } \right\} $ from $ U(0,\theta)$. Let ${Y}_{i}$ be the order statistics. Then the sufficient statistic for $\theta$ is ${ Y }_{ n ...
1
vote
1answer
66 views

Interval of non-uniformly distributed set of numbers adjusted that it properly excludes extremes

Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution: numbers 1, 2 and 3 about 20 occurrences number 6 has 2 occurrences and number 9 has only ...
0
votes
1answer
50 views

Finding probability of uniform random variable given a condition with another random variable

Suppose X and Y are independent and uniformly distributed on the unit interval (0,1). Find: $$P[Y>\frac{1}{2}\,|\,Y>1-2X]$$ How I approached it was to find the area where $Y > 1 - 2X$, and ...
0
votes
0answers
48 views

Goodness of fit for uniform distribution

I have a set of $N$ votes $O_1, O_2,..O_N$ distributed into $n$ bins. So... $$n \le N$$ $$0 \le O_i \le N$$ $$\sum_{i=1}^{n} O_i = N$$ I want to generate some sort of metric for how uniformly ...
0
votes
1answer
31 views

Finding variance .

Suppose that $f : [0, 1] → [0, 1]$ and we wish to estimate $$I = \int_{0}^{1} f(x) dx$$ Using the hit-and-miss method, we obtain the estimate $$\hat I_{HM}=\frac{1}{n}\sum_{i=1}^{n}X_i$$ where ...
0
votes
1answer
139 views

Plot the cdf and simulate a random variable (rv) with this cdf using the inversion method.

Consider the continuous random variable with pdf given by: $$f(x) = 2(x − 1)^2;\quad 1 < x ≤ 2$$ $$f(x) = 0;\quad \text{otherwise}$$ Plot the cdf for this random variable. Show how to simulate ...
1
vote
2answers
55 views

$X$ is half normal and $S ∼ U{(−1, +1)}$. How $Z = SX ∼ N(0, 1)$?

If we chop a standard normal distribution in half and use only the positive side (scaled up by a factor of $2$ to maintain a proper density), then we get the so-called ‘half normal’ density: ...
0
votes
2answers
327 views

Uniform Distribution : pdf & inverse cdf

$X\sim U(1,3)$. Verify that X has cdf $F_X(x) = 2(x − 1)$ for $x \epsilon(1, 3)$ and thus that $F^{−1}_X (y) = 2y +1$ for $y \epsilon (0, 1)$. My attempt for ...
-2
votes
1answer
168 views

Convolution of Discrete Uniform ,$DU$, Distribution.

If $X\sim DU(k,a,h),\quad -\infty<a<\infty,h>0=1,2,\ldots$ then the probability function is $$P(X=a+jh)=\frac{1}{k},\quad j=0,1,\ldots,k-1$$ Let $Z\sim DU(r,0,s)$ and $Y\sim DU(s,0,1)$ , ...
1
vote
2answers
48 views

Number of times you have to make a bet on a uniform distribution to expect to achieve a minimal result

Edited for the sake of clarity: If you have a random variable $Q$ distributed uniformly on some interval, say $[a,b]$, what is the function $f$ that describes how many times you have to draw on the ...
2
votes
0answers
177 views

Max variance of uniform distribution?

Suppose I roll a 20-sided die 1000 times and count the number of times a particular value comes up. This gives an array of 20 counts, and the expected value of each is 1000/20 = 50. I'd like to find ...
5
votes
2answers
4k views

Probability density function of a product of uniform random variables

Let $z = xy$ be a product of two uniform random variables, with $x$ having the range $[a, b)$ and $y$ the range $[c, d)$. What is the probability density function of $z$, and how is it calculated?
3
votes
1answer
478 views

Distribution of Sum of Discrete Uniform Random Variables

I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution? Thanks!
0
votes
1answer
237 views

How do you generate mean from a uniform distribution between 0 and 1

How do you generate mean from a uniform distribution between 0 and 1 with a sample size of 10? using excel? Do you have to first generate random numbers from 0 to 1?
0
votes
1answer
184 views

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 ...
1
vote
1answer
416 views

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 ...
0
votes
1answer
599 views

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 $m\in\mathbb{N}$ ...
2
votes
2answers
830 views

Finding the mean of a uniform distribution?

I have a random set $\{a,b,c\}$ and a second set $\{e,d\}$ I draw one number first number and one from the second Letting $X_1$ denote the first number and $X_2$ the second number find, $E(X_1)$ and ...
3
votes
2answers
757 views

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 ...
1
vote
1answer
101 views

Measure the uniformity of distribution of points in a 2D square

I am currently running into this problem: I have a 2D square, and have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out ...
3
votes
2answers
121 views

Why is $P(X<0)$ the same as $P(X\le 0)$ for continuous distributions?

In uniform distribution, a continuous distribution, for example where $A = -1$ and $B = 1$, $P(X < 0)$ is said to be the same as $P(X \le 0)$. Why is this?