# Questions tagged [discrete-distributions]

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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 ...
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 : ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
24 views

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### 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 ...
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, ...
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 ...
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.
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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} ...