Tagged Questions

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Say (X,Y) has the distribution on the area shown below find P(X>1|Y=1/2) [closed]

Say (X,Y) has the distribution on the area shown below, find P(X>1|Y=1/2)![enter image description here][1]
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uniform distribution over disk

Given two independent random variables $A$ uniform on $[0,1]$ and $B$ uniform on $[0,2\pi]$. Obtain the joint pdf, tranform to the disk, if necessary modify to obtain the uniform pdf over the disk. ...
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What is the pdf of $X,Y$?

We know that the common pdf of $X,Y$ is constant function, on the triangle $(0,0),(0,1),(2,0)$ (and out of this range the value of the function is zero). What is $f_X(x)$ and $f_Y(y)$? My solution: ...
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PDF of sum of two random variables

Assume an $n$ dimensional random variable $U$ that is uniformly distributed in the volume of an $n$-sphere with radius $R$. Assume another $n$ dimensional random variable $N$ that is distributed ...
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Uniform distribution over an hyper-ellipsoid

Let $\mathbf{X} \in \bf{R}^p$ be a random vector whose elements are uniformly distributed over the hyper-ellipsoid $x^TAx<1$, (where $A$ is a positive-definite matrix). Is it possible to compute ...
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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]. ...
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Convolution of two Uniformly distributed r.v. ove

Assume a continuous random variable $X$ that is uniformly distributed $\underline{\text{on}}$ a $k$-sphere. For simplicity, lets assume a simple circle with radius $R$ in 2 dimension. Therefore ...
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Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i)$. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
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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 ...
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P.d.f. of $XY$, where $X, Y$ are independent uniformly distributed over $[0,1]$ [duplicate]

I tried to change the variables: Let $U=XY$ and $V=Y$; so then the Jacobian is $1/v$. So joint pdf $g(u,v) = f(x,y)\cdot (1/v) = 1/v$ Would you then integrate over $v$ from $0$ to $1$ to get the ...
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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 ...
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Fast uniformity test within a ball.

Assume I have a dataset lies within a ball centered around the origin, I want to test the uniformity of the point distributed in the ball. In addition, I have all the distances to the origin computed ...
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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 ...
Let $U_{1}\sim U(0,1)$ be a standard uniform random variable. Is $U_{1}-U_{1}$ uniformly distributed? I've been trying to work this out as follows: Let $A,B$ be rv's $$P(A-B\leq ... 0answers 56 views Uniform Distribution Probability A manager of an apartment store reports that the time a customer on the second floor must wait after calling the elevator has uniform distribution ranging between 0 and 6 minutes. Assuming that it ... 2answers 34 views Independent two random variables with uniform density Let X \sim U[-1,1] and Y=X^2. Show that X and Y aren't independent. Of course we have F_X(x) = \frac{x+1}{2} and F_Y(y) = \frac{\sqrt{y}+1}{2}. But how can I find$$F_{XY}(x,y) = \Pr(X ...
A line segment AB of length 1m is broken in two at a random point P where the length of AP has the following probability density function: $f(x)=6x(1-x), 0<x<1$ A point Q is uniformly selected ...