# Questions tagged [multinomial-distribution]

Questions in probability which includes more than one random variable

113 questions
Filter by
Sorted by
Tagged with
26 views

### entropy of weighted sampling without replacement

Let us have $k$ elements of weights $w_1,…,w_k$. We sample elements with weights without replacement. At the first, the probability of element $i$ to be sampled is $w_i / \sum_{l=1}^k w_l$. Then, the ...
8 views

### Parameter estimates and uncertainties associated with a Multinomial distribution

I have a process/model the depends on a single parameter $\lambda$ that generates $n+1$ outcomes. From $N$ events I can estimate the probabilities $\hat{p}_k$ from $N_k/N$ using a MLE for a ...
220 views

### On asymptotics of certain sums of multinomial coefficients

Given positive integers $n$ and $k$, set $$S_{n,k}=\sum_{\substack{a_1+a_2+\dots+a_k=2n\\ a_i \in 2\mathbb{N},\,i=1,\ldots,k}}\frac{(2n)!}{a_1!a_2!\dots a_k!},$$ where $2\mathbb{N}=\{0,2,4,\ldots\}$....
• 327
22 views

### Power average of multinomial distribution

Given a multinomial distribution $$X = \left(X_{1},\ldots,X_{K}\right),\ \sum_{k = 1}^KX_{k} = n,\quad\mbox{and}\quad p_{1} = \cdots = p_{K} = \frac{1}{K},$$ I wonder whether there is some ...
• 115
12 views

### Necessary condition for constrained optimization

Suppose $X=(X_1, \cdots,X_k)$ follows the multinomial distribution with a known size $n$ and an unknown probability vector $(p_1,\cdots,p_k)$. Find the necessary conditions for the solution to the ...
• 1,708
1 vote
72 views

### Multinomial example from online game [closed]

Suppose that a multinomial distribution has 25 outcomes, the first 24 have chance $\frac{1}{465}$ and the final has $\frac{441}{465}$ chance. Find $n$ the number of trials for this such that the ...
• 3,914
62 views

### Multinomial distribution: probability that at least one outcome didn't occur

I'm trying to find the probability, that in a group of $N$ people, there are no people from at least one district with populations $n_{i}$ (for $i \in \mathbb{N}$ ranging from $0$ to $k$, where $k+1$ ...
• 120
41 views

### Finding probability from Dirichlet distributions under constraints

Suppose that I have the following: Three Dirichlet distributions of dimension k: distr1, distr2, distr3 A vector A of dimension 3 and a vector B of dimension k. Does anyone know about an algorithm ...
99 views

### Multinomial probability calculation [closed]

$10$ cars choose uniformly at random between three parking lots ($A$, $B$, and $C$). Calculate the probability that none of the parking lots are empty and that there are exactly $5$ cars in lot $A$. ...
• 3
1 vote
78 views

### Probability of average of N samples of an unfair dice bigger than 5.

Imagine we have a dice: Side probability 1 0.1 2 0.1 3 0.1 4 0.1 5 0.2 6 0.4 We will throw the dice N times (ie. 7 times) And we want to calculate the probability that the average of the 7 ...
29 views

### How to write the distribution of $(x_1,x_2)$ given $X_3=x_3$

Let $x=(x_1,x_2)$ be a trinomial distribution with parameters $(n;p_1,p_2)$. Deterine the conditional distribution of $(x_1,x_2)$ given $X_3=x_3$. Remember $X_3=n-x_1-x_2$. How do I write the ...
16 views

• 111
53 views

### Multinomial distribution question

Let there be 12 different events with different probabilities of happening, each of which is known to us. How do we then find the probability that all the events happen at least once for a given ...
86 views

### Multinomial distribution - closed form for $P(X_1 = X_2, \dotsc, X_{2n-1} = X_{2n})$

Let $n, k \in \mathbb N$ and $(X_1, \dotsc, X_{2n}) \sim \operatorname{Multinom}(2k, p_1, p_1, \dotsc, p_n, p_n)$. Is there a closed form of  P(X_1 = X_2, \dotsc, X_{2n-1} = X_{2n}) = \sum_{k_1 +...
• 47
159 views

### Distribution of $X_1+ X_2$ when $X_1, X_2, X_3$ follows a multinomial distribution

The setting is that $X_1,X_2,X_3 \sim Multinomial(n;p_1,p_2,p_1+p_2)$. So the constraint is that $X_1+X_2+X_3=n$, and $p_1+p_2+(p_1+p_2) = 1$. I don't really understand how I should go about finding ...
• 639
235 views

### Cumulative Multinomial Distribution does not seem to add up to 1.00 for parameters >3

For a multinomial distribution $P = ( n! / (\prod_{i=1}^k {n_i!}) ) * ( \prod_{i=1}^k {{p_i}^{n_i}})$ If you sum the resulting multinomial distribution for every possible unique frequency for k=2 for ...
• 123
42 views

• 103