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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Joint density function of $f_\theta(x) = \theta x^{\theta-1}$

Let $f_\theta (x) = \theta x^{\theta-1}$, where $0
Nerd
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Geometric Expectation

Two coins with heads probabilities $\frac{1}{3}$ and $\frac{1}{4}$ are alternately tossed, starting with the $\frac{1}{3}$ coin, until one of them turns up heads. Let $X$ denote the total number of tosses, including the last. Find: $$E(X)$$ I have…
Fototekt
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Nearest neighbor distribution seems to fail empirical test

I'm attempting to use the nearest neighbour distribution to understand the separation between uniformly distributed points in a high-dimensional space. I find that there is discrepancy between empirical results and the analytic distribution and…
Josh Albert
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Conditional distributions for a multinomial random variable

I'm struggling to understand how to solve the following problem. We have (1,2,3,4) is a multinomial distributed r.vs with parameters =10 and p =(1 =0.3,2=0.3,3=0.3,4=0.1). Now I need to find P(1=3,2=3,3=3|4=1). I would know how to approach this if…
LushyIvy
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Can't find name of specific probability formula, very similar to geometric distribution

I'm not exactly attempting to answer a textbook or school question, this is something I'm attempting to figure out for my own sake - so there isn't a written question to use as an example. I'll do my best to explain. I am attempting to get an event…
chronoquairium
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how do determine the distribution of outcomes for a given probability?

For a game I generate various block types given certain odds. Say, there's a $0.001$ chance for the karma block. If a typical game has $600$ blocks, what's the distribution of games that have $0$ karma blocks, $1$ karma blocks, $2$ karma blocks,…
HappyEngineer
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Show that normal distribution has 0 mean and unit variance

For a normal distribution, $$\phi(x)=\frac{1}{\sqrt{2\pi\sigma^2}}\times e^{\frac{-1(x-\mu)^2}{2\sigma^2}}$$ Question:Prove that the standard normal distribution has 0 mean and unit variance?
Avv
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Scale a set of weights so that the ratio between them is larger and more pronounced?

I am attempting to generate a set of weights to supply to a loss function for my neural network. This network attempts to categorize pixel values between a set of classes. This set of classes is unbalanced in the number of samples. For example say I…
KDecker
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How to find density function?

$X \sim N(1,4)$ and $Y = 3 - 5X$. How to find the density function of $Y$? I tried first to find the distribution function of Y, but got stuck. $$F(y) = P(Y <= y) = P(3 - 5X <= y) = P(X >= (-y + 3)/5).$$ Any help appreciated.
user62136
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Distribution of 25 book titles between 4 different authors

Can someone please help me? I've been trying to do this for hours: You are part of a reading group. Each member will read a book from 1 out of 4 different authors(W,X,Y,Z). In how many ways is it possible to select 25 books from theses authors so…
user850676
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Gaussian expectation of an exponential function

I am struggling to prove this, $$ \int \mathcal{N}_\mathbf{x}(\mu,\Sigma)e^{a^T\mathbf{x}}d\mathbf{x} = e^{{a^T\mu}+\frac 12a^T\Sigma a} $$
ahmetbulut
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Estimation of marginal and conditional frequency distribution

The joint frequency distribution of two discrete random variables, and , is given in the following table: Can anybody help me how to find the marginal frequency distributions of and and the conditional frequency distributions of given =1, and…
silent_hunter
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How does the y-axis of a probability density function compare to a histogram?

I had a bit of a question about fitting probability density functions (specifically the Weibull Distribution) to a set of data. I have seen a number of examples where the distribution is directly overlaid on the histogram and they both share the…
user863345
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What's the usage of knowing $p(\ln\sigma) = \text{const}$ in noninformative prior

In the PRML equation 2.239, for a non-informative prior of a scale parameter, the probability mass for interval $A \leq\sigma \leq B$ and $A/c\leq \sigma \leq B/c$ for any choice of all A and B should be the same. Hence $p(\sigma) \propto…
Kelvin_neverKnow
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Relationship between number of trials and complementary CDF of a binomial distribution

I have a question related to Binomial distribution. Can someone help me? Consider the following complementary CDF of a binomial distribution with parameters n and p : $$ \bar{F}(x) = \sum_{k=x+1}^{n}(^n _k)p^k(1-p)^{n-k} $$ Is the complementary CDF…
Sreekz
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