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. ...
1
vote
1answer
112 views

Find probability that a given number of events occur when each event has a different probability [duplicate]

Say I have three independent events with a probability of .25, .5, and .75 chance success for the individual events. How would I determine the probability that 0, 1, 2, or 3 of the events are ...
68
votes
18answers
89k views

Statistics interview questions

I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this ...
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 ...
14
votes
5answers
3k views

Probability that number of heads exceeds sum of die rolls

Let $X$ denote the sum of dots we see in $100$ die rolls, and let $Y$ denote the number of heads in $600$ coin flips. How can I compute $P(X > Y)?$ Intuitively, I don't think there's a nice way to ...
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 ...
9
votes
2answers
3k views

Risk of extinction of Schrödinger's cats

I am interested in how uncertainty can be accounted for when considering the risk of extinction of a species. Forgive me for extending a rather tired thought experiment, but at least it's familiar ...
9
votes
2answers
5k views

How to model the sum of Bernoulli random variables for dependent data?

I have almost the same questions like this: How can I efficiently model the sum of Bernoulli random variables? But the setting is quite different: $S=\sum_{i=1,N}{X_i}$, $P(X_{i}=1)=p_i$, $N$~20, $...
3
votes
0answers
1k views

Approximate a poisson binomial distribution with a binomial distribution?

I have samples of Bernoulli distributed variable that are neither the first nor the second i in iid. My goal is to model their sum. I got from Wikipedia that I can use the poisson binomial ...
2
votes
2answers
354 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 ...
3
votes
1answer
309 views

X is binomially distributed, and Y is binomially distributed. What distribution does X+Y follow?

We know that $X$ follows $\mathrm{Bin}(n_1,p_1)$, $Y$ follows $\mathrm{Bin}(n_2,p_2)$, $X$ and $Y$ are independent. What does $X+Y$ follow? I know the answer, that if $p_1=p_2=p$ then $X+Y$ follow $\...
3
votes
0answers
617 views

Why does the accuracy of the central limit theorem for a mean depends on the skewness of the random variables being summed?

The accuracy of the central limit theorem for a mean depends on the skewness of the random variables being summed. Could someone explain that to me? Or could someone propose a book to read? Thank ...
2
votes
1answer
357 views

Efficiently computing poisson binomial sum

Suppose there is a match between two teams where the first team to win a certain number of games wins the match. The match is handicapped, with Teams A needing to win $H_A$ games and Team B needing $...
2
votes
0answers
431 views

What is the distribution of independent binomial variables conditional upon the sum?

Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim \operatorname{Binomial}(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is ...
1
vote
1answer
246 views

How can I efficiently approximate the sum of Bernoulli random variables for any number of summands in partial sum?

I have almost the same question as: How can I efficiently model the sum of Bernoulli random variables? But: (1) The number of random variables for summation is ~ N=20 (case 1) or N=90 (case 2). (2) $...

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