# Questions tagged [cumulative-distribution-functions]

For questions related to cumulative distribution functions.

469 questions
Filter by
Sorted by
Tagged with
8 views

### Clarification about inequality in summation

In my work I am facing the following situation, wherein I am trying to compute CDF of random variable $Y$ such that $F_Y(y) = \text{Pr}(\sum_{m = 1}^M |Z_m|^2\leq \frac{y}{A})$ -----(1) where $Z$ is a ...
25 views

### Finding the best formula for this case lottery algorithm?

there, sir. I'm a Developer and now working on a project. So the problem is... A program generates a 6-digit number for a winning ticket with each digit between a range of (0-9). Then user buys some ...
17 views

39 views

### A mistaken proof that CDFs are not right-continuous

While trying to prove that CDFs are right-continuous, I wrote the following proof which seems to actually prove that CDFs are right-continuous if and only if the measure of the given point is zero. I’...
7 views

### Measuring half-lifetime from 1-cumulative or frequency distributions, what's the difference?

I have a question that is blowing my mind. Let's say that I measure a phenomenon that has a duration in seconds. I can graph the data as a frequency distribution (a histogram), showing a nice ...
36 views

### two-dimensional version of "$F_X(X)$ is uniformly distributed"?

It is a well-known fact in probability theory that if $X$ is a continuous random variable and $F_X$ is a cdf of $X$, then $F_X(X)$ is uniformly distributed over $[0, 1]$. Is there a two-dimensional ...
19 views

### Integral on triangle Bivariate

I can't see why the integral $$J=P(Z_1>0,Z_2>0,Z_1+Z_2<1)$$ can be computed as $$J = \left(F(\frac{1}{\sqrt{2}})-\frac{1}{2}\right)^2 \qquad (*)$$ where $F$ is the cumulative probability ...
29 views

### Conditional distribution of $Z$ given $Z=X$

Given that $X$ and $Y$ are independent exponential random variables with parameters $\lambda_1$ and $\lambda_2$. If $Z=min(X,Y)$, find the conditional distribution of $Z$ given $Z=X$ My try: I found ...
28 views

### How to find the CDF of $Y=\frac{1}{2}X$?

Let $X$ have an exponential distribution with rate parameter $\lambda=\frac{1}{2}$ I believe that the probability density of $X$ is $$f_X(x) = e^{-x/2}$$ So the CDF of $X$ is then $$F_X(x)=-2e^{-x/2}$$...
1 vote
34 views

### CDF and cumsum of a prbabolity density function

This is a really really stupid question, but why when I plot a CDF and cumsum of a PDF (e.g. exponential): $$f(t) ~ = \lambda e^{-\lambda t}, ~~~ t \ge 0$$ I get ...
26 views

11 views

### Conditional survival function in landmark analysis

In H.Putter & H.C. van Houwelingen's paper "Understanding Landmarking and Its Relation with Time-Dependent Cox Regression" the authors state that the conditional survival function, given ...
30 views

### Partial derivatives of a Black-Scholes solution of a "cash or nothing" call option

Currently working on a problem sheet that asks us to find the partial derivative $\frac{\partial C}{\partial r}$ of the following formula for the price of a "cash or nothing" call option: \...
21 views

### How to find the tail of cdf for the distribution?

I don't know how to derive the tail of cdf for this situation: We do a Bernoulli experiment every $\frac{1}{n}$ seconds, the probability of success is $\frac{\lambda}{n}$. $Y_n$ is the waiting time ...