Questions tagged [discrete-distributions]
The discrete-distributions tag has no usage guidance.
71
questions
0
votes
0answers
34 views
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 ...
1
vote
1answer
20 views
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 :
...
0
votes
1answer
60 views
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 ...
0
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0answers
29 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 ...
1
vote
1answer
33 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 ...
2
votes
1answer
39 views
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 ...
1
vote
1answer
31 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 ...
1
vote
1answer
32 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 ...
1
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0answers
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 ...
0
votes
0answers
22 views
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, ...
0
votes
1answer
24 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 = \...
0
votes
0answers
47 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 ...
1
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0answers
25 views
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 ...
4
votes
0answers
67 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 ...
1
vote
0answers
19 views
What type of regresion for discrete quantitave dependent variable [closed]
I need to make a regression. My dependent variable is a quantitative and it can take 5 possible values. I am asking what type of regression can I use.
Thank you for your help.
2
votes
2answers
53 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) &...
2
votes
1answer
22 views
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 ...
2
votes
0answers
20 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 ...
3
votes
2answers
339 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"
...
1
vote
1answer
23 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 ...
0
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0answers
28 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 ...
1
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0answers
24 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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0answers
25 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$$
Here $...
1
vote
1answer
31 views
What is the name and formalism of this discrete distribution? [closed]
I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)).
I calculated (brute-forced with a script) the probability of k positive ...
0
votes
1answer
53 views
What distribution is $P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x$?
What kind of distribution is the following:
$$
P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x
$$
and how can I find $P_X(x < x_0 \mid K, N)$?
0
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0answers
36 views
Test for null hypothesis: the rank of each variable is uniformly distributed
Assume the following situation:
I have $N$ samples of $k$ continuos variables, $$x_n = (x^n_1,...,x^n_k).$$
I do not trust whether I can combine the continuos variables across samples, but I want to ...
3
votes
1answer
71 views
Expression for Probability of Being Between Two Poisson Random Variables?
I have two independent Poisson random variables $A \sim \text{Poisson}(\lambda_A)$ and $B \sim \text{Poisson}(\lambda_B)$. For a fixed given integer $k$, I'd like to determine
$$P(A < k \leq A + B)....
0
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0answers
17 views
Distribution of Independent but Non-Identically Distributed Geometric Random Variables?
What distribution describes the sum of independent but non-identically distributed geometric random variables? That is, (abusing notation a little) if $\{X_n \sim Geometric(p_n)\}_{n=1}^N$, what ...
1
vote
0answers
25 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, ...
4
votes
1answer
50 views
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 ...
2
votes
1answer
25 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.
2
votes
1answer
49 views
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 ...
1
vote
1answer
87 views
Can we always write a random variable as conditional expectation plus error?
Consider the random variables $Y,X$. I believe that we can always write
$$
Y=E(Y|X)+\epsilon
$$
with $E(\epsilon|X)=0$.
Question: Is the above true regardless whether $Y$ is a discrete or continuous ...
2
votes
1answer
87 views
Parameterized probability distribution for finite, discrete values?
Sorry if I don't have the right terminology for asking this question in a good way ...
I'm curios if there is an established distribution function for the following case:
I have 20 different options, ...
5
votes
4answers
547 views
If $X$ and $Y$ have the same marginal distribution, then do they have to have the same conditional distribution?
Suppose $X$ and $Y$ are two random variables that have the same distribution. Does
$$P[X \leq t \mid Y=a]$$
be necessarily equal to $$\;\ P[Y \leq t \mid X=a]?$$
Note that if $X$ and $Y$ are bivariate ...
0
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0answers
53 views
joint PDF of continuous and discrete random variables
Given exponential a random distribution X with PDF $f_X(x)=\lambda e^{-\lambda x}$ and a random variable Z with the PMF $p_Z[z]=0.5, z= \pm1$, I am trying to find the PDF of $Y=ZX$ (I also know that Z ...
7
votes
2answers
103 views
Let $X,X_1,X_2,X_3,...$ be positive integer random variables. Show that $X_n \overset{d}{\to} X$ implies $\lim_{n\to\infty} P(X_n=k) = P(X=k)$
Question
Let $X,X_1,X_2,X_3,...$ be positive integer random variables. Show that $X_n \overset{d}{\to} X$ implies $\lim_{n\to\infty} P(X_n=k) = P(X=k)$.
The $\overset{d}{\to}$ denotes convergence in ...
0
votes
1answer
64 views
Sufficient Statisitics and Discrete Distributions
I am trying to master minimal/complete sufficient statistics, however I am having trouble when the distributions are discrete and involve indicator functions. Here is my 3 part question:
Let $X$ be a ...
0
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0answers
45 views
Generating correlated discrete random variables
Suppose that we have $q_t \in \{-1, 1\}$ where $\mathbb{P}(q_t = -1) = \mathbb{P}(q_t = 1) = \frac{1}{2}$. Further, assume that
\begin{align}
Cor\left( q_t, q_{t-k} \right) =
\begin{cases}
...
3
votes
1answer
89 views
Sufficient Statistics and Discrete Distributions
Let $X_1, \ldots, X_n$ be a random sample of size $n$ from the following distribution:
$$f(x;\theta) = \left\{\begin{array}{ccc} \frac{1 - \theta}{6} & , & x = 1 \\ \frac{1 + \theta}{6} & ,...
3
votes
1answer
84 views
Conditional expectaction with probabilities for a sum of independent random variable
I have a r.v $S_N$ built as a sum of Bernoulli with parameter $p$. So $S_N = X_1 + X_2 + \ldots + X_N$. There is a second variable N, such that $N \sim Poisson(\lambda) $.
I have to compute:
$P(S_N=0)...
2
votes
0answers
46 views
Maximum entropy discrete distributions with specified mean
Consider a discrete distribution on {1, ...,n}, with mean given as $m$, what is the maximum entropy distribution?
I know it takes the form $p_{X}(k)=ar^{k}$ and is a geometric distribution when n is ...
0
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0answers
23 views
In poisson distribution why does setting r = mean_value not output 50%?
If I want to find probability of 10 cars passing highway checkpoint in 60 seconds where on average 10 cars pass in 60 seconds.
Assuming there is no rush hour I can use Poisson distribution
So lambda =...
0
votes
0answers
26 views
If $Y$ is continuous and $X$ is discrete, how to write the joint density of $(Y,X)$?
If $Y$ is continuous and $X$ is discrete with a finite number of points in the support, how to write the joint density of $(Y,X)$?
For example, to write the joint density function evaluated at $(Y,X)=(...
1
vote
1answer
159 views
intuition behind Brier score
Assume that we have some count data $x_{1}, \dots, x_{n}$, which take values $\{1, \dots, m\}$
and we have some estimator of the probability mass function, $\hat{\mathbf{p}} = (\hat{p}_{1}, \dots, \...
3
votes
2answers
196 views
Do financial return series have a probability mass function (pmf)?
Stock returns, computed from stock prices as $r_t = \ln (p_{t}) - \ln (p_{t-1})$, are real-valued and unbounded giving the impression that they are continuous random variables. But aren't they ...
2
votes
2answers
230 views
Is there a discrete distribution I can use for sampling in R?
Firstly, I don't have a stats background, so please accept my apologies for any errors or misunderstandings in the question below.
I'm trying to use R to draw values from a discrete probability ...
1
vote
1answer
59 views
guessing a number between 1 and 100
Person A chooses an integer between 1 and 100 at random, then B can guess that number in (at most) 7 attempts, i.e. $\log_2(100)+1=7$. What if now A chooses an integer from a distribution that is ...
1
vote
2answers
264 views
How to know whether a zero-inflated model is the way to go? Both poisson and negative binomial do not fit my count data
I have a dataset with count data as response variable ranging from 0-5 (number of chicks fledged). I intend to carry out a GLMM and need to know which distribution my data follows. I used the descdist(...
2
votes
1answer
205 views
Intuition for expectation of discrete random variable that takes positive integers
If $X$ is a discrete random variable that takes values on the positive integers, it is true that
$$E(X) = \sum_{k=1}^{\infty} P(X \ge k)\;.$$
I know how to prove this (by expressing the summand as a ...
