# Questions tagged [cumulative-distribution-functions]

For questions related to cumulative distribution functions.

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### Probability of an event not recurring [closed]

If I have a vector consisting of ones and zeros, where the weight of ones is at the beginning and the weight of zeros is at the end of the vector, when can I be confident (e.g., 95%) that there will ...
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### Generalized equation for bivariate normal distribution

I would like to know how to derive the CDF of a bivariate probit model as shown below: $p^{y_{1},y_{2}} = \Phi(2c_{1} - 1*x_{1}\beta_{1},2c_{2} - 1*x_{2}\beta_{2}, (2c_{1} - 1)*(2c_{2} - 1)*\rho)$ ...
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### CDF of the sum of independent r.v.

I was wondering if there's a known relationship between $F_{X+Y}$ and $F_X+F_Y$, when $X, Y$ are independent r.v. (or even comonotonic r.v.) Thanks in advance!
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### Calculating Correlation Given Joint Cumulative Distribution Function

I am interested in computing $Corr(X,Y)$ for $0 \leq x \leq 1$ and $0 \leq y \leq 1$, given two cases: firstly, $F_{X,Y}(x,y)=min(x,y)$ and secondly, $F_{X,Y}(x,y)=xy$. How would I go about doing ...
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### Subtract two normal cumulative distribution functions rather than plotting a normal one to compare a binomial with a normal variable?

In order to understand the Central Limit Theorem, I am comparing a $Binomial(n,p)$ variable with a large $n$ and a normal variable with mean $\mu p$ and a standard deviation $\sigma = \sqrt{np(1-p)}$. ...
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### Find CDF of a uniform distribution between 2 values

So, I've been struggling on a problem that goes like this: X is a random variable with this probability density function: ...
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### Can you find out what the cumulative distribution function is if you know the random variable X?

I have a theoretic question on my probability class. Suppose that you know the X random variable. Can you calculate the cumulative distribution function? If not, why not?
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### Solving Normal Probability Distribution (PDF) and Cumulative Probability Distribution (CDF) for given X and comparing to Excel's NORM.DIST() function

I have been trying to understand and implement the Excel function NORM.DIST(x, mean, standard_deviation, cumulative) in another programming language. There exist ...
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### Numerical evaluation of cumulative gaussian distribution function for a particular correlation matrix

I'm looking for an efficient numerial method to calculate the cumulative multivariate distribution function for normally distributed random variables with correlation matrix \begin{equation} \mathbf{\...
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### how to calculate the cumulative distribution function of sums of n Bernoulli distribution?

I'm a beginner on statistics. And I come up with this question when studying Bernoulli distribution: Let $X_n$ be the sum of $n$ independent trials of a Bernoulli experiment, whose result can be $1$ ...
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### How are the Probability Measure and Cumulative Distribution Function linked when calculating the Expectation of a RV X?

Given a probability space $(\Omega, \Sigma, P)$ and a measure space $(\mathbb{R}, \mathcal{B}(\mathbb{R}))$, let $X: \Omega\rightarrow\mathbb{R}$ be a RV which is $(\Sigma, \mathcal{B}(\mathbb{R}))$-...
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### Find $\alpha$ and $\beta$ so that $f_X(x)$ can be a density function.

\begin{equation*} f_X(x) = \begin{cases} \frac{4x^2}{5} & \text{ , if } 0 < x \leq 1\\ \alpha(5-2x) & \text{ , if } 1 \leq x < 2\\ \beta x^2 & \text{...
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### the composition of a random variable and its cdf

Let $X$ be a continuous random variable. Let $F(t)=P(X\le t)$ be the cdf (cumulative distribution function) of $X$. Then the random variable $Y=F(X)$ takes values in the unit interval $[0,1]$. What is ...
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### Maximum Likelihood of P(x<a) = a and P(x<a) = a^2 number generators given a sample

The question asked: There are two number generators. Given a sample, which of these generators is it from? 1) generates a random number uniformly between 0 and 1 with $P(x<a) = a$ 2) generates a ...
### X is a Random Variable taking values {1,2,…} with P(X=k)=$c/[k(k+1)]$
Show $P(X\ge k)=c/k$ I tried getting the integral for $X\ge k$. Didn't work out. $$\int_k^{\infty} c/k(k+1)dk=-c*ln(|(1/\infty)+1|)+c*ln(|(1/k)+1|)$$ Which equals $c*ln(|(1/k)+1|)$, which I don't ...
### The $L^1$ distance of two CDF is the $L^1$ distance of the quantile function coupling
In a book I found the following exercise: Let $F,G$ be two cumulative distribution functions. Then \int_0^1 \vert F^{-1} (t) - G^{-1} (t)\vert \text d t = \int_\Bbb R \vert F(x) - G(x) \vert \text ...