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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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Average angle in a square

Consider a unit square $OABC$ where,$O\equiv (0,0),A \equiv (1,0),B \equiv (1,1), C \equiv ()$.If two point $P_1$ and $ P_2$is chosen randomly and uniformly in or on the square.how do we find the expected value of angle $\angle P_1OP_2$? My…
AgnostMystic
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why inverse of CDF generates the samples of PDF

I programmed the "inverse transform sampling" according to its wikipage. It sounds amazing: Given a PDF: $$ p(x) $$ we can generate the samples by $$ s= F^{-1}(r) $$ where $r\in (0,1)$ is a uniform distribution and F(x) denotes the CDF of p(x). I…
whitegreen
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Poisson process of alternating sources, pairing products of the two of them

I have a problem I've been thinking for a while, but it's confusing me quite a lot. There are two independen machines, A and B. A produces a product at a rate of 2/minute, and B does it at a rate of 3/minute, both of them following a Poisson…
FDrico
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Deriving a new distribution from repeated samples

it's been many moons since I've been in a math class, so I'm not sure how to formulate the problem precisely. I'll describe it informally instead. This is related to response times in a computer system. Let's say I have some system, foo, that I can…
Olaf
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What is this type of distribution called?

I have a collection of 1000 balls. Some of the balls are light grey, and some are dark grey. All of the light grey balls are exactly the same shade of light grey. Ditto the dark grey ones. Some of the balls are heavy, and some are light. Again, the…
Rocketmagnet
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find the distribution

Suppose two teams play a series of games, each producing a winner and a loser, until one team has won two more games than the other. Let G be the total number of games played. Assume each team has a chance of 0.5 to win each game, independent of the…
kris91
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If X and Y are independent exponential random variables with pdf $f(x) = 0.5e^{-0.5x}, x\geq 0$, find $P(X>1, Y>4)$

My thinking: $\int_4^\infty\int_1^\infty 0.5e^{(-0.5x)} \,dxdy= $ $\int_4^\infty e^{-0.5} dy $ but when I integrate this I get $e^{-0.5}y\Biggr|_{4}^{\infty}$ which equals $\infty$ what am I doing wrong?
user839486
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Need intuition help with exponential distribution and help solving a problem

This is one of the question asked in my textbook I am able to solve this using Poisson distribution but can't solve it using exponential distribution The distance between major cracks in a highway follows an exponential distribution with a mean of…
user788888
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If $X \sim \chi^2$ with $n$ degrees of freedom how is the distribution of $-X$?

If $X \sim \chi^2$ with $n$ degrees of freedom then how is the distribution of the random variable $-X$? I think that $-X \sim \chi^2$ with $-n$ degrees of freedom but I dont sure.
wessi
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Random Sampling of Beta Distribution using direct method

I have been reading about generating random samples using direct methods. I have come across a definition that if, $X_i ~ Unif(0,1)$ and are i.i.d., then: \begin{align} Y = \frac{\sum_{i=1}^m logX_i}{\sum_{j=1}^{m+n} logX_j} \end{align} will be a…
Abijith P Y
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Argument that maximizes a continuous distribution

I have a continuous of $X$, $f_X$. Now I want to find the argument that maximizes $f_X$, i.e., $\arg \max_x f_X$. I know that for a continuous distribution, the probability for $X = x$ is 0. Thus, I think we can replace $\arg \max_x f_X$ with simply…
Bikas
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X is a continuous random variable with $Y = (X − 3)^2$

If $X$ follows $N(0,1)$ what is the mgf of Y? I think I found that the pdf of Y is $\frac{1}{\sqrt{2y\pi}}e^{(\sqrt{y}+3)t}e^{\frac{-(\sqrt{y}+3)^2}{2}}$ Then I think you're supposed to integrate but the integral doesn't work out well.
ramseys
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Mathematics behind structural reliability analysis

In structural engineering we have to accept the fact that you can never be exactly sure how much load a structural member can resist, that the load carrying capability of an element is not one exact value but distributed with some probability…
S. Rotos
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If second quartile is equal to fourth quartile can we prove the third quartile?

Given than the Q2 = Q4 = 17 but the sample size is 15, but the elements and the Q3 is unknown Can we just say the Q3 = 17?
aukk123
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Comparing two normal distribution, repeated several times

You and your friend bowl every week. Your average score per game is normally distributed with an average value of $175$ and a standard deviation of $30.$ Your friend's score per game is normally distributed with an average value of $150$ and a…
Natasha
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