In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. (Def: http://en.m.wikipedia.org/wiki/Binomial_distribution)
Questions tagged [binomial-distribution]
2213 questions
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binomial distribution formula - factorial cancellation
This is confusing me in Intro to Stats course.. any help in explaining is appreciated!
Binomial Distribution formula:
$\frac{n!}{(n-k)!k!}$
For 125 Coin Flips w/ 3 Heads = 317,750 (n = 125, k = 3)
Steps to…
Cory Robinson
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PFG of Y~Bin(n,p)
Let $X_1, X_2, \ldots , X_n \sim \operatorname{Ber}(p)$ be iid Bernoulli random variables.
(a) Determine the probability generating function of $Y \sim \operatorname{Bin}(n, p)$.
I understand that for $X \sim \operatorname{Bin} (n,p)$, the general…
dstar19
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Convergence in probability for binomial distribution
If $m$ is the number of success in $n$ independent trials, in which the probability of success is $p$, then how to prove that $\frac mn$ converges in probability to $p$ as $n\to\infty$.
user3575652
- 347
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average euclidean distance between vector of coin flips
I have a biased coin with the probability of flipping heads as $p$. I have a room of $n$ people and they each have this same coin. I ask everybody to flip their coins, and record their results as an $n$-dimensional vector of ones (heads) and zeros…
wenhoo
- 117
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Distribution Function of Binomial Random Variable
Let $X$ be a random variable with probability mass function $p_k= \binom n k p^k (1-p)^{n-k}$ (binomial). If $F$ is the corresponding distribution function, find the distribution of $F(X)$.
I know for certain that I need to get the sum of $k$…
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Probability of m successes in n Bernoulli trials with unknown success probability Q∼Uniform(0,1)
I am working on a problem involving Bernoulli trials with an interesting twist. Here's the setup:
$n$ independent Bernoulli trials are conducted.
The success probability $Q$ is unknown and follows a uniform distribution between $0$ and $1$.
What…
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binomial question PROOF style
Take the number $n$ of stages of a binomial variable $X \sim B (n, p)$ to be fixed, and allow $p$ to vary. $p$ is not the random variable of this binomial experiment - $X$ is - but "allow $p$ to vary" means "consider a binomial experiment $X \sim B…
moon river
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Conditions for a Binomial Random Variable
I understand for a random variable to be distributed binomially:
There must be n fixed trials
Each trial must be independent of the others
Probability of success must remain constant throughout the trials
Outcome either happens or doesn't…
kiwizor
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Suppose U∼Binomial(n,p) and n>2. What is P(U>1)?
I'm confused on how you can interpret $n>2$. I want to use $\mathbb{P}[U>1] = 1 - (\mathbb{P}[U=1] + \mathbb{P}[U=0])$ but not sure how to implement $n>2$ into the formula.
Any ideas?
Tingo Hugo
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Binomial distribution greater than
If $n = 6$ and $p = 0.50$, what is the probability that $x ≥ 1$?
$P(x ≥ 1 | n = 6 \,\text{and}\, p = 0.50) = ?$
Attempt:
$p=0.5$
$n=6$
$x=1 \,\text{or}\, 2$ etc
$(\frac{n!}{x!(n-x)!})(p^x(1-p)^{n-x})$
So I calculated 0.0938 for 1 and 2,3 etc etc but…
JanusP
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An apple garden claims that only 3 percent of its apple have a brown spot,
An apple garden claims that only 3 percent of its apple have a brown spot, the apples are sold in a lot of 2000. the garden agrees to take back any lot that contains more than 80 apples with spots.
Let $X$ denote the number of apples in a lot that…
Myshkin
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Having dificulty to figure out event and other variables in binomial distribution
A company is selling 105 tickets to a plane that has 98 seats because only 85% of the buyers actually take the flight. What is the probability that even taking this approach 3 seats will be unused?
For me the sucess would be 15, the number of the…
Diego Alves
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What is $k$ for in the Expectation of Binomial Distribution
In the proof of the Expectation of Binomial Distribution, why there is a $k$ in the following equation? I understand the part is the probability (PMF) of Binomial Distribution.
But the random variable X should be either 0 or 1. Where is this $k$…
CyberPlayerOne
- 617
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What is the probability of getting $8-6$ (Win-lose), when you bet $14$ times in a win or lose game with $60$% winning percentage?
What is the probability of getting $8-6$ (Win-lose), when you bet 14 times in a win or lose a game with $60%$ winning percentage?
According to the answer, it must be $ 17.4$%.
I tried to solve this using binomial distribution but my answer is not $…
AYA
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Why is expectation for binomial distributions linear (intuitively)?
In the post by André Nicolas, in this stack, he writes that the expectation is a linear operator on events. This I can not understand, what exactly is intuitive explanation of expectation being linear? or, maybe some motivation to describe it as…
tryst with freedom
- 11,538