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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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Translation Invariance of Time Change of Brownian motion

I'm kind of not 100% sure about this: Let $B$ be a Brownian Motion defined on some Probabitlity space $(\Omega, \mathscr{F}_t,\mathbb{P)}$ and $\phi^{-1}:\mathbb{R}\rightarrow\mathbb{R}$ increasing continuous function. Is it true that for any…
K. N.
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The lifetime of two parallel connected diods

Consider two diods connected in parallel. Suppose the life times T1,T2 of each diod have the same distribution function F.What is the life time T of the whole system? What is the distribution of T? My intuition was that T= Max (T1,T2) because it is…
Yilin Wang
  • 307
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Why is it that you can change the PDF/PMF argument for related random variables to produce new PDF/PMF equality statements?

For random variables $$N_1 \sim P(\lambda_1)$$ $$N_2 \sim P(\lambda_2)$$ $$N \sim P(\lambda)$$ where $N=N_1+N_2$ and $N_1$, $N_2$ are independent. Why is the following statement true? $$P(N_1=n_1)=P(N=n,N_2=n-n_1)$$ In other words, why is the…
kfs
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Probability for continuous uniform distribution from $0$ to $10$

Suppose $X$ has a continuous uniform distribution on the interval $[0, 10]$. Calculate: $Pr(X+\frac{10}{X}>7)$.
S. Smith
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Probability (Uniform, exponential, or something else?)

I want to find the distribution of the question. A student uses a computer for an average of 10 minutes. Let X denote the amount of time that a student uses the computer in a single session. Confusing me with distribution and parameter.
Cheesy Williams
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Fitting distribution

I have the following distribution of points and I need to fit a theoretical distribution. It looks like Gamma but I am not entirely sure. Do I have to fit several of them (like Exponential, Poisson etc.) to rule them out or is there a generalized…
user2167741
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Binomial distribution question Holiday resort overbooking

The question: A hotel has 230 rooms and uses an overbooking policy. The probability that a customer cancels or does not show up at the hotel is 0.12. Find the maximum number of rooms the hotel can book and still be 85% sure everyone who turns up…
vexs
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Joint and conditional distributions of multiple variables

If I have three random variables $X, Y$ and $Z$ where $Y$ and $Z$ are independent. Is it true that $P(X,Y,Z)=P(X,Y)P(X,Z)$? What about $P(X\vert Y,Z)=P(X\vert Y)P(X\vert Z)$?
Daisy
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expectation of the log of the binomial distribution

Suppose $X\sim binomial (n,0.5)$ and set $Y=log(X)$ (base 2 is better, but any base would do). How do I compute the expectation of $Y$, or find a good lower bound? Thanks.
mike
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Likelihood of continuing a discrete series

If I have a series like "aaabbbabaabaabbaa" and I'd like to know whether next element in series is "a" or "b", would a Poisson distribution be best solution for this? If so, checking Poisson for "3" wouldn't be right since it can be >3 in the…
Marin
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joint probability

I read the following problem and I cannot get the right solution: We consider a system of 12 sensors. The probability of one sensor to detect a signal with a magnitude higher than a is $p=\frac{1}{2\pi }\int_{x=a}^\infty \exp(\frac{-x^2}{2})$. What…
user5452
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Manipulating a random variable that is uniformly distributed

I had to answer the following question: $X$ has a uniform distribution between 0 and 1. What is the distribution of $X^3$? Now the pdf for X is simply: $f(x)= \left\{ \begin{array}{ll} 1, &\mbox{if } 0\leq x \leq1 \\ 0, & \mbox{otherwise} …
Vladimir Nabokov
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Distribution of a random variable to the power of 3

I have to answer the following question: $X$ has a uniform distribution between 0 and 1. What is the distribution of $X^3$? I'm not looking for an answer, just want to know how I should begin to answer the question. Now the pdf is…
Vladimir Nabokov
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What is support of sum of two random variable

Suppose there is random variable $K= X + Z$ $$P(X=x)=\frac{T\lambda^{x/\alpha}}{(k/\alpha)!}e^{-T\lambda}\quad(x=0,\alpha,2\alpha,......)$$ $$P(Z=z)=\frac{\lambda^{z/\beta}}{(z/\beta)!}e^{-\lambda}\quad(z=0,\beta,2\beta,......)$$ $$X=\alpha…
Kim
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How to cluster words using Jensen-Shannon Divergence?

I'm working on a project that requires text analyzing. I'm currently trying to extract keywords from a single document. I referred to this thesis(Keyword Extraction from a Single Document using Word Co-occurrence Statistical Information by Matsuo)…
Joe Wong
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