Linked Questions

4
votes
1answer
108 views

Probability mass function with variable probability? [duplicate]

I would like to calculate the probability of a certain result coming out at least 'x' times in 'n' attempts when the probability of result varies on every attempt; all attempts are independent events. ...
2
votes
1answer
288 views

Probability distribution for varying probabilities in R [duplicate]

I'd like to plot the probability distribution for a set of binomial trials in R, the catch is that each trial has an independent probability of success (which I have in vector form). So, in R if I ...
1
vote
0answers
12 views

The probability of at least N positive outcomes where all experiments have different probabilities [duplicate]

Let's say we bet on 10 different soccer matches. The probability of our team winning, for each game, is 0.17, 0.78, 0.41, 0.79, 0.47, 0.08, 0.29, 0.30, 0.35, and 0.54. What is the probability of ...
40
votes
9answers
11k views

How can I efficiently model the sum of Bernoulli random variables?

I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where $\...
46
votes
5answers
31k views

Probability distribution for different probabilities

If I wanted to get the probability of 9 successes in 16 trials with each trial having a probability of 0.6 I could use a binomial distribution. What could I use if each of the 16 trials has a ...
15
votes
2answers
27k views

Sum of Bernoulli variables with different success probabilities [duplicate]

Let $x_i$ be independent Bernoulli random variables with success probabilities $p_i$. That is, $x_i=1$ with probability $p_i$ and $x_i=0$ with probability $1-p_i$. Is there a closed expression or an ...
8
votes
1answer
8k views

Efficient convolution (in R)

I want to calculate/evaluate the convolution $$g(x)=\int_D f(x-t) \phi(t) dt,$$ where $f$ is a density and $\phi$ is a smooth function with compact support $D$. The convolution is not available in ...
5
votes
1answer
491 views

Probability of at least $k$ Bernoulli successes with varying probabilities conditional on an event

Suppose a female in a given species has, on a given year $x$, PMF $Bernoulli(f(x))$ of finding a mate given she doesn't yet have one. Once she finds a mate, she doesn't need another. This same ...
2
votes
2answers
356 views

Distribution of a linear combination of Bernoulli random variables?

I am trying to calculate the expectation of absolute value of a linear combination of independent Bernoulli random variables, $E(|a_1x_1 + a_2x_2 + ...+ a_nx_n|)$. In particular, $(a_1, ..., a_n)$ are ...
1
vote
1answer
686 views

Probability of completing N events

I'd like to calculate the probability that at least N independent events out of a set of M events complete successfully. Each event Ei has a probability of success of Pi. For example, if there are ...
4
votes
2answers
142 views

Estimate Number of Party Guests

You are throwing a party and want to know how many guests you can expect. You are inviting $N$ persons, each person has a probability $x_i$, $ 1 \leq i \leq N$ of showing up and $x_i$ is between 0 and ...
4
votes
2answers
121 views

Calculate percentiles of probabilistic functions

For easier understanding, let's assume we talk about sport betting. There are 3 independent games with team_A winning with a probability of 70%, 50%, 10% respectively. Each bet has its odds (odds_1, ...
0
votes
1answer
57 views

Frequency of N Independent Events

I'm attempting to implement a numerical approximation to assess the frequency of outcomes given $N$ independent random variables. There is a slight twist however, each $N$ has a weight, Each variable ...
2
votes
0answers
38 views

How can I estimate the number of correct guess right based on varying probabilities for each independent event?

Assuming that we have a model that outputs these (binomial) probabilities for 10 independend events: 0.89, 0.69, 0.41, 0.92, 0.43, 0.52, 0.90, 0.98, 0.56, 0.85 I would like to know if there is a way ...