Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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Help with integration of joint pdf to find $P(T_3 - T_2 \gt T_1)$

I have a joint pdf $f(x_1,x_2,x_3) = e^{-x_1 -x_2 -x_3}I(x_1 \ge 0)I(x_2 \ge 0)I(x_3 \ge 0)$ and I want to calculate the probability $P(T_3 - T_2 \gt T_1)$ where $T_1 \lt T_2 \lt T_3$ are the order statistics. so I calculate the joint pdf…
tim.mof
  • 59
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distribution of (inverse) distribution function

Let $F: \mathbb R \rightarrow [0,1]$ be strictly monotonic increasing distribution function. The random variable $X$ has distribution function $F$ and the random variable $U$ is uniformly distributed on $[0,1]$. I want to determine the distributions…
xxx
  • 645
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how to find curve where ratio of all points are on a specific curve?

I've done some research and gathered data for plotting on a histogram. I believe it is a bell-shaped curve, but given what I know am not sure. I know it is centered around 0, with half of it negative and the other half is positive. The distribution…
d l
  • 173
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about a difficult and weird Probability question

Let W be the random variable that counts the number of tails before one gets r heads for a coin whose probability of heads is θ. Without using moment generating function, show that the mean and variance for W are [r(1-θ)]/θ and [r(1-θ)]/θ^2 Please…
SeanZ
  • 31
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some well known distribution?

I calculated the discrete probabilities for my project. I have two parameters k and l and I varied the third one which is the y axis (x values are log of the probabilities) in this enclosed picture. The computation is quite expensive so I would…
harmonik
  • 11
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1 answer

Probabability of Joint Distribution

Let the continuous random variables $X$ and $Y$ have the joint probability density function given by $f(x) = 3/2x$ for $00.5)$. This was how I approached the problem. But I know that Pr $(x<1.5 and…
J.R.
  • 179
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Find the Conditional Probability

Let the continuous random variables $X$ and $Y$ have the joint probability density function given by $f(x)$ = $kx$ for $0
J.R.
  • 179
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Independence of continuous random variables squared

If I know that two continuous random variables $X$ and $Y$ are independent, are $X^2$ and $Y$ necessarily independent? Are $X^2$ and $Y^2$ also independent?
jamaicanworm
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2 answers

Finding a constant from a continuous distribution

$X$ is a continuous random variable with PDF $$f(x) = c\theta^{|x|} \quad \text{ for } -\infty
user2850514
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How do you compute the PDF of a function of 2 random variables that is not a sum?

If you have a random variable U(X,Y) that is a function of two other random variables X and Y such that $U(X,Y)=X+Y$ and you know the PDFs of X and Y are defined to be exponential such that $f(t) = \lambda e^{-\lambda t}u(t) $ then you know…
user11460
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Distribution function for price of stock.

I want to create a function to create stock prices over a period in Excel. What is the distribution of a stock price?
user184539
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Regarding Asymptotic Behaviour of normal distibution

If $x_n -> \infty$ in such a way that $x_n^3/ \sqrt{n} -> 0$, then P{$S_n^*$ > $x_n$} ~ 1 - F($x_n$) where $S_n^*$ is the standard normal variable and F is the normal distribution function. (Note: This is a theorem and it has been discussed in…
Sriram Natarajan
  • 275
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Conditional probability of a training sample

Let $\mathcal{D}=\{ (y_1,x_1), ..., (y_N,x_N) \}$ be i.i.d. training data. Let $\widetilde P(Y,X)$ be the empirical distribution. The goal is to maximize the likelihood of $P(\mathcal{D}|\;\Theta)$. I am having difficulties with this…
j-a
  • 338
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a simple question about probability density function

Given $F(x)$ is the value of the distribution function of the continuous random variable $X$ at $x$, what should be probability density of $Y=F(X)$?
johnny
  • 197
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how to solve this probability density function

Let X have the probability density function given by: f(x)=$\frac{4}{\beta^3\sqrt{\pi}}x^2$exp{$\frac{-1}{\beta^2}x^2$} from 0< x < $\infty$ a)Verify that f(x) is a probability density function. b) Find E(x) and Var(x). My first impression was…
J.R.
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