# Questions tagged [cumulative-distribution-functions]

For questions related to cumulative distribution functions.

615 questions
Filter by
Sorted by
Tagged with
1 vote
20 views

### Find the behaviour of the cumulative conditional function and match it to a known distribution

The given joint distribution is: $$f_{X, Y}(x, y)=\frac{n 2 a^2 x^{n-1}}{y^{n+3}} I_{[0, y]}(x) I_{(a, \infty)}(y), n \in \mathbb{N}$$ The exercise asks us to find the cumulative distribution of the ...
1 vote
23 views

1 vote
99 views

24 views

### Taxi Stand Waiting Time: CDF Calculation

I'm having a problem understanding this solution. Let's say this solution is correct. If you take the the derivative of the resulting CDF you should get the correspoding PDF. In this case the PDF ...
17 views

### During the process of simulating an exponential random variable

According to the text book, to get a associated CDF $$F_x$$ is given by $$F_x(a)=\int_{-\infty}^af_x(x)dx=1_{[0, +\infty)}(a)\int_0^a\lambda e^{-\lambda x}dx=1_{[0, +\infty)}(a)(1-e^{-\lambda a})$$ ...
1 vote
53 views

### Finding parameters in piecewise CDF [closed]

The CDF of a continuous random variable X is: $$F_X(x) = \begin{cases} 0, & \text{if } x < 4 \\ Ax+B+\frac{C}{x} ,& \text{if } x \geq 4 \end{cases}$$ (a) Find the parameters A, B,...
1 vote
69 views

### Probability over $\Bbb R$ and density

Let $P$ a probability over $(\Bbb R, \mathcal B)$ where $\mathcal B$ are Borel set, $f:\Bbb R \to \Bbb R$, $f\geq 0$ almost everywhere s.t. $\forall a<b$ rational $$P([a,b]) = \int_a^bf(x)dx$$ ...
28 views

### Understanding an expectation formula

Consider a puddle of water which evaporates at random points over time. Let $f(x,t)$ be the fraction of evaporated water at site $x$ on the puddle at a time $t$ after the start of evaporation. I want ...
1 vote
44 views

### Uniform Sampling points on a line using 2 Uniform distributions

I have been struggling with this problem for quite some time but I am not sure how to proceed. So I am given a sampling algorithm : We would like to uniformly sample points on a line between A and B. ...
1 vote
26 views

47 views

73 views

### Expected value of max function of a random variable: understanding the proof

Consider a random variable $\phi$. Assume $\mathbb{E}[\phi]<\infty$. Let $F_\phi(t)$ be its cumulative distribution function. Let $(a)^+=\max\{0,a\}$. I am trying to understand the proof of the ...
1 vote
42 views

### Joint CDF of two random variables - rectangular region equation

I just started learning about joint CDFs and I think I understand the concept, but I don't understand this equation in my textbook regarding a rectangular region. Why are the top right and bottom left ...
1 vote
30 views

1 vote
42 views

Let Say, $G \left(x \right)$ is the Cumulative distribution function of a random variable $X$ which is continuous, now consider below integral $\int_{0}^{\alpha} 1 \left(G \leq u \right)du$, where $1 \... 2 votes 1 answer 69 views ### Is there a non-trivial max invariant family of distributions? The Problem Traditionally, the value of a position in a chess engine is computed as the maximum of the values of the subsequent positions. These values are typically represented as a single number. ... 1 vote 0 answers 42 views ### First order stochastic dominance with binary interaction I have two variables$X_1$and$X_2\in [0,1]$, where$X_2$(strictly) first order stochastically dominate (FOSD)$X_1$, i.e.,$F_{X_2}(x) \leq F_{X_1}(x)$for all$x$. Then I have,$Y$and$Z$, ... 1 vote 0 answers 61 views ### Stochastic ordering of dependent random variables given their sum and a common copula I am interested in pointers for the stochastic ordering of continuous dependent variables with common copulas. I have a vector$X=(X_1,X_2,...,X_N)$and a vector$Y=(Y_1, Y_2, ..., Y_N)$. X and Y ... 0 votes 1 answer 30 views ### Example for Helly's Selection Principle Helly's selection principle(in the context of Probability Theory and not Functional Analysis) gives that if$F_{n}$be a sequence of CDF's then there exists a subsequence$F_{n_{k}}$such that$F_{n_{...
My lecture notes gives the following definition of convergence in distribution of $\mathbb{R}^k$-valued random variables ($x \leq y$ for $x,y \in \mathbb{R}^k \Longleftrightarrow x_i \leq y_i$ for all ...
Does it exist a non discrete random variable with CDF $F$ with the following hypothesis : $F$ is constant in a neighborhood of each point of continuity I had the idea of Cantor function but it does ...