Questions tagged [discrete-distributions]

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We have a 4 sided die, a 6 sided die and a 12 sided die. We roll a die twice and get 1 and 5. What's the probability that we rolled the 6 sided die?

I'm trying to solve this question but I'm not sure about my thinking. So I think what I need to compute is : $$P[\text{rolled the 6 sided die} | \text{got numbers 1 and 5}]$$ I tried to do it with the ...
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1 vote
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Confidence intervals for integer parameters

I'm interested, purely out of curiosity, in what methods can be used to calculate confidence intervals for discrete integer model parameters. As an example, consider the model (which I can flesh out ...
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8 votes
2 answers
366 views

Regression model for integer response

Let the response be $Y_i \in \mathbb{Z}$ and the covariate $X_i \in \mathbb{R}^p$. For counting data where $Y_i$ are restricted to be nonnegative, we have Poisson regression or negative binomial ...
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Joint distribution of two discrete random sample

Assume $x_1$ and $x_2$ form a random sample from the following discrete distribution: $ \quad x| \qquad 1 \quad 2 \quad 3 $ $\, P(x)| \quad .1 \quad .2 \quad .7 $ How can I find the joint ...
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Ways to measure deviation from a discrete uniform distribution [duplicate]

I'm looking for a way to characterize the deviation from a discrete uniform distribution. Example: 50 balls are distributed over 10 urns. In the most equal case, all urns get 5 balls. In the most ...
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1 vote
1 answer
38 views

Construction of statistics of a discrete distribution

I have the following problem: we consider an i.i.d sample $\mathbf{X} = (X_1,...,X_n)$ of the discrete set $\{1,...,N\}$. An agent has to infer the probability distribution of $X_i$. I wanted to use ...
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3 votes
1 answer
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Which is the correct solution to the hypothesis testing: $H_0 : \lambda =65, H_1 : \lambda >65$ , $X$ is a Poisson ($\lambda$) ,$\alpha=0.05$

Given the following hypothesis test: $H_0 : \lambda =65, H_1 : \lambda >65$ , where $\lambda$ is the parameter of an $X$ distributed as a Poisson $\alpha=0.05$ . We have n=10 samples. Using as ...
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How to validate the decomposed distributions?

I am fitting distributions for the time spent for three processes (i.e., pick up tools, walk to destination, install) in a system that I am trying to simulate where the original data for these ...
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2 votes
2 answers
61 views

Showing that $E[\hat{\tau}_D] = P(n_D > 0)\tau_D$ and $\vert E[\hat{\tau}_D] - \tau_D\vert \leq \tau_D(1-\frac{N_D}{N})^n$

Consider the following double sampling scheme: We have a population of size $N$ with variable of interest $y_i$ for each $i \in \{1,\dots,N\}$, and (fixed) subpopulation $D$ of size $N_D$. Let $S$ ...
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What metric is best fitted for comparing encodings?

I am trying to compare two distributions, that each correspond to different numerical encodings, e.g. compare fp32 encodings to various other encodings on a same set of values. However I do not know ...
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Can we use Dirichlet process to simultaneously estimate the number of mixtures and component distribution of a Bernoulli mixture?

Suppose I have a random sample on a Bernoulli random variable $\{X_i\}_{i=1}^N$ generated from model $p=\sum_{k=1}^K\pi_kp_k$,where $p\equiv Pr(X=1)$ and $p_k\equiv Pr(X=1|k)$, and $\pi_k$ are the ...
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11 votes
3 answers
685 views

How do you calculate the expected value of a discrete distribution without replacement?

Say I have a set of 10 values I want to draw 3 values from, uniformly, without replacement. For instance: $$S = \{0,0,0,0,22.95,0,0,0,19.125,25.5\}$$ With replacement, this seems simple, you just add ...
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1 vote
2 answers
67 views

Goodness-of-fit tests for discrete distributions

I have data where only values at large x should fit to a particular distribution whose parameters I wish to determine. I want to do a goodness-of-fit test to find the value of x where the data fit to ...
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1 vote
1 answer
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If hitting a target has $P = 0,3$, how many shoots to get at least one hit with a probability of $0.9$?

Cheers, I know that hitting a target has a probability of $0,3$, and I am asked to find the number $n$ of times that I have to shoot at the target to get at least one hit with a probability bigger ...
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1 vote
1 answer
114 views

randomized Neyman-Pearson lemma for a discrete distribution

We let $\Theta=\{0,1\}$, and $X$ be a discrete R.V with the following probability distribution: x 1 2 3 4 5 6 7 8 $f(x;0)$ 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.86 $f(x;1)$ 0.14 0.12 0.10 0.08 0.06 ...
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1 vote
1 answer
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Distibution of the number of trials required to see all possible outcomes

In the simplest case given a set of N items is the distribution for the number of draws with replacement before all items are seen? This is the case I really need. More generally what is the ...
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38 views

KS test or chi square for comparing two distributions of a discrete ratio variable

I have a discrete ratio variable (length) from two samples and I'd like to know if the distributions are different or the same. In my case length is discrete because it can only take on integer values ...
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1 vote
0 answers
47 views

Approximating a countable-state (infinite) Markov model with a finite-state one

TL;DR—in a nutshell I have a countable-state Markov model (with a countably infinite number of states) in which the probability of transitioning to states $S_{i>k}$ for large $k$s are practically ...
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1 vote
1 answer
81 views

Central limit theorem for independent, non-identically distributed, finite discrete random variables

I am positive, that there exists a version of CLT stating that, the distribution of the sum of infinite many independent, nonidentical, finite discrete random variables, is Gaussian. I just could not ...
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3 votes
2 answers
193 views

Sampling from a Poisson distribution (infinite support)

I would like to sample from an infinite discrete distribution, i.e. Poisson distribution \begin{align} \Bbb P(X=k)=e^{-\lambda}\frac{\lambda^k}{k!} \end{align} where $\lambda$ is a fixed parameter. In ...
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Probability of independent transmission attempts (independent Bernoulli trials)

I am trying to figure out the independent transmission attempts (independent Bernoulli trials) probability $q$ for a sender node to remain in the same (waiting) state if receiving node is in sleep ...
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1 vote
1 answer
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How to random generate a sample from {0,2} in R? [closed]

There are some solutions online on how to do a random generation of the discrete uniform distribution, but only on consecutive integers. Like : ...
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1 answer
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How to solve the probability of N events occurring at the same time, N is a random variable [closed]

How to solve the probability of N events occurring at the same time, N is a random variable and its PDF is known. The probability of each event is also known and the probability of each event is not ...
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0 answers
38 views

How to calculate the variance of drinks orders?

I'm taking a stats course on LinkedIn's learning site and they provide this problem. Calculate the variance of the drinks orders in the following table. The idea being to figure out the variance of ...
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1 vote
1 answer
63 views

Joint PMF of two order statistics with discrete parent distributions

Let $X_1, X_2$ be i.i.d from a discrete distribution with finite support with cumulative distribution $F(x)$ and probability mass function $f(x)$. Let $X_{1:2}$ and $X_{2:2}$ represent the order ...
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3 votes
1 answer
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What is the distribution of the difference of two independent multinomial random variables?

Say I have two independent random vectors $X_c$ and $X_f$. The random vector $X_c$ is composed by three random variables: $X_{1c}$, $X_{2c}$ and $X_{3c}$. The second random vector $X_f$ is composed by ...
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1 vote
1 answer
33 views

Odds that 5 persons share the same last name given a group of n people

What are the odds that 5 individuals share the same last name, say Miller, in a group of 50 assuming the associated probability of 'Miller' in a population being 2%. How do I calculate it? Thought ...
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1 vote
1 answer
56 views

Variance of discrete distribution exceeds variance of discrete uniform distribution

I am not a mathematician, so I don't quite understand how comes that a variance of some discrete probability distribution could exceed the variance of the discrete uniform distribution. I thought that ...
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1 vote
0 answers
8 views

How to measure degree of groupings

I have a set of boolean data where I'm trying to distinguish between data where the values are uniformly distributed and data where the same class is grouped together. e.g 1001010011 seems pretty ...
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0 answers
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How to generate uniformly distributed random numbers between 1 and 26 with a dice [duplicate]

I want to generate uniformly distributed random numbers between 1 and 26 with a dice: Is this correct: I have assembled the following algorithm using the Monte Carlo Method: {1, 2, 3, 4, 5, 6} {7, 8, ...
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0 votes
1 answer
31 views

Probability of not picking a row in a random draw where the number of rows are N

There are $N$ rows :$R_1, R_2,R_3,..., R_N$. What is the probability of not picking a row in a random draw? My try and understanding : Let $X$ be a random variable which is defined as follows: $$X = \...
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0 votes
1 answer
106 views

Why aren't Normalizing Flows suitable for Discrete Distributions?

I am currently trying to understand why normalizing flows are not applicable to discrete distributions (a quick primer on NF can be found here). The assumptions on the transformation f between the ...
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1 vote
0 answers
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Multi-Multi-Class Classification

I'd like to build a model that can output results for several multi-class classification problems at once. Suppose you have diagnostic data about a product that needs to be repaired and you want to ...
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4 votes
0 answers
104 views

distribution bootstrap sample median

I am interested in the conditional probability that the median $X^*_{(m)}$ of a bootstrap sample $X_1^*,\ldots,X_n^*$, where $n=2m-1$ for integer $m$, equals the $k$th order statistic $X_{(k)}$ of the ...
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2 votes
2 answers
80 views

Approximating non-integer median for CDF of discrete variable

In my googling, it seems the proper way to find the median of a cdf of a discrete variable is to stick to the discrete values provided, even if you overshoot and end up with an x where P(X <= x) &...
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2 votes
1 answer
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The Description of the Variable of Interest: Binomial VS Negative Binomial Discrete Random Variables [duplicate]

Does it makes sense to say that: In a binomial distribution we looking for the number of successes in a given number if trials, and in a negative binomial distribution we are looking for the number of ...
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2 votes
0 answers
22 views

Need help choosing which random variable distribution to use

I have these two questions. A department store claims that 80% of its customers pay their credit card on time. If you want to calculate the probability that at least 6 out of 11 customers pay their ...
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3 votes
2 answers
1k views

Kernel Density Estimation for a Discrete Variable

I was tying to estimate the distribution for a discrete variable. However, suddenly I thought that "Is a simple histogram sufficient? because I have observations for every evaluation point" ...
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1 vote
1 answer
24 views

Test whether probabilities of heads are under-estimated across many coins

I am trying to figure out a problem that is equivalent to the following. Suppose you have a bag of $n$ coins in which each coin is labelled with a probability $p_i$ that it will come up heads when you ...
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0 votes
0 answers
38 views

How to assess if a distribution has significantly changed over time

I'm studying the incidence of different types of influenza in a country over several years. In particular, for years from 2015 to 2020 I know the relative abundance of 3 types of influenza (% of ...
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1 vote
0 answers
26 views

I don't need a full solution but i need guidance for the solution [closed]

I don't need a full solution but I need guidance for the solution.
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0 answers
50 views

MLE and binary variables

Suppose $z$ and $y$ are discrete random variables taking values 0 or 1. The distribution of $z$ and $y$ is given by $$P\{z=1\}=\alpha$$ $$P\{y=1|x\}=\frac{e^{\gamma x}}{1+e^{\gamma x}}\\ z=0,1$$ Here $...
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1 vote
1 answer
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What is the name and formalism of this discrete distribution? [closed]

I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)). I calculated (brute-forced with a script) the probability of k positive ...
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1 answer
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What distribution is $P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x$?

What kind of distribution is the following: $$ P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x $$ and how can I find $P_X(x < x_0 \mid K, N)$?
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0 votes
0 answers
50 views

Test for null hypothesis: the rank of each variable is uniformly distributed

Assume the following situation: I have $N$ samples of $k$ continuos variables, $$x_n = (x^n_1,...,x^n_k).$$ I do not trust whether I can combine the continuos variables across samples, but I want to ...
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3 votes
1 answer
78 views

Expression for Probability of Being Between Two Poisson Random Variables?

I have two independent Poisson random variables $A \sim \text{Poisson}(\lambda_A)$ and $B \sim \text{Poisson}(\lambda_B)$. For a fixed given integer $k$, I'd like to determine $$P(A < k \leq A + B)....
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3 votes
0 answers
59 views

How to prove or disprove that a complete sufficient statistic exists?

We have a discrete random variable which takes values with probabilities $p, q, p+q$ and $r$. I want to construct a complete sufficient statistic based on a single observation from this distribution, ...
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4 votes
1 answer
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Finding the mode given the probability of occurence

When a teacher asks a question, a student has a probability of 0.4 of being asked. Assume the occurrence is independent. What is the mode of the number of questions raised by the teacher it takes for ...
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2 votes
1 answer
27 views

Does $ \sum_a P(a|b,c)P(d|a) = P(d|b,c)$?

I saw it applied in a textbook once, but can't seem to figure out why or if it holds.
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2 votes
1 answer
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Convolution of probability mass functions (3 non-parametric distributions)

I am familiar with the convolution of probability mass function when it involves two random variables, but I get a little confused when there's a third one. I have to find the probability mass ...
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