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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What is the probability of two two-digit integers, with reversed digits (i.e., 13 and 31) appearing in a set of two integers?

What is the probability of two two-digit integers, with reversed digits (i.e., 13 and 31, or 45 and 54) appearing in a set of two integers? Assume the first integer in the set of two can be any integer between 00 and 99 (inclusive). The second…
Jety Lefr
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I'm confused about whether the probability distributions i used on this problem are correct

Problem: There are $7$ keys in a brelok, from which only one opens the door. Find the average number of attempts that we will need in order to open the door and the probability to need exactly $5$ attempts, when everytime we try a key: a) We remove…
Than1
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Trying to rank the distribution of events over time

I am trying to figure a way to rank a set of financial trades done across multiple instruments. This takes place across of a period of 1 year. For each instrument, there is a list of trades that are either positive or negative. I am trying to find a…
Thomas
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Variables Chosen From An Arbitrary Distribution

Let $D(\mu, \Sigma)$ represent an arbitrary distribution with mean $\mu$ and covariance $\Sigma$. I am given that $\beta_k$ is a vector of length $M_k$: $$\beta_k \sim D\left(0, \frac{\sigma^2_k}{M_k} I_{M_k} \right)$$ where I am given the value…
mathz2003
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Why is t distribution leptokurtic?

Why is t distribution leptokurtic? It lies below normal and approcahes standard normal as degree of freedom increases so it should be platykurtic.
Ankita Goyal
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drawing at least 90% of colors from urn with large populations

My problem is: suppose I have an urn containing balls of $n = 10000000$ (i.e., $10^7$) different colors, with $1000$ balls of each color (so the total number of balls is $1000n = 10^{10}$). Suppose I draw $100000000$ (i.e. $10^8 = 10n$) balls. My…
Danny Bennett
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Prove that a characteristic function is constant

Let $f(t)=Ee^{itX}$ be a characteristic function. Assume that $f(t)=1+\phi(t)+o(t^2)$, where $\phi(t)$ is odd, i.e. $\phi(t)=-\phi(-t)$. Prove that $f(t)=1$, $\forall t$ The assumption means that $E\cos(tX)=1+o(t^2)$ i.e.…
Xiong Jiangnan
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Matching pdf with the Inverted Gamma Distribution

So the Inverted Gamma probability density function is: $\displaystyle{f(x; \alpha, \beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{-\alpha - 1}\exp\left(-\frac{\beta}{x}\right)}$ The equation I'm dealing with is: $\displaystyle{f(\sigma; ?, ?) =…
Trts
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How a uniform distribution may induce different solution regarding Bertrand's paradox

I have a neophyte question regarding the formulation of the Bertrand's paradox. This is related to the definition of what we call a uniform distribution. If we consider the 3 point of views of “random endpoints” method, “random radius” method and…
Alain Bensoussan
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Probability mass function of bank loan, find expected payment.

We have a random variable X that is the number of months that a certain owner of an estate needs to pay a loan in the Bank if he/she has a contract with insurance company to help him/her to pay a loan. X's probability mass function…
Michael Vie
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Exponential Random Variables

QUESTION: Let $X$ and $Y$ be exponentially distributed random variables with parameters $a$ and $b$ respectively. Calculate the following probabilities: (a) $P(X>a)$ (b) $P(X>Y)$ (c) $P(X>Y+1)$ ANSWER: (a) since $X$ is exponentially distributed, we…
Natalie
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Distribution of an additional random variable

I need a little help for the following exercise: Let $X_1, X_2,\ldots$ be sequence of iid rv with values in $\{1,2,3 \}$ and $p(i):=P(X=i) \gt 0$ for $i \in \{1,2,3\}$. Define an another rv $R:=\inf\{n\in \mathbb{N}:X_n\in\{2,3\} \}$ a) Show that…
jed
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Best Distribution to Approximate this Histogram

Given the histogram below, what common distribution would be well fit to this data i.e. Beta, skewed normal. I want to use the data as a prior in Bayesian analysis so want to approximate it by a distribution in the exponential family to make this…
rwolst
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Meaning of uniform distribution

I'm studying stochastic calculus now. And I found in my textbook that strictly review elementary probability theory. But I suddenly confused the notion of uniform distribution. I thought when we see uniform distribution on the 2 dimensional space,…
user13232877
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MGF and characteristic function of a sum of iid random variables

Suppose $X_1,X_2,...X_n$ are iid random variables with the density $$ f(x)=2x ,\,0 \leq x \leq 1.$$ Define $$Y= X_1+X_2+...+X_n.$$One way to find the expected value of $Y$ is to first find the mgf of Y using…
AgnostMystic
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