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
7
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How to use Pascal's triangle for binomial expansion
The question is asking for me to expand ${(p+r)}^4$. I know that I have to use Pascal's triangle, the fourth set down, which is $1,4,6$,$4,1.$ My thinking is that I have to use these numbers to solve this through synthetic division, but don't really…
Clay
- 73
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4 answers
Proof of the normalisation of the Binomial Theorem
I was going through a stats book yesterday when I saw the normalisation of the binomial distribution stated. I was wondering if anyone had a proof of that please?
$$
\sum^{n}_{r=0}p^{r}(1-p)^{(n-r)}\cdot{^{n}C_{r}}=1.
$$
I can see how this…
James
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Spacial Conditional Binomials
Consider the random variable $X\sim B(n,p)$ and also $Y\sim B(n-X,q)$, how can we express $Y$?
we know that for the case $Y\sim B(X,q)$, $Y$ is a simple binomial variable with distribution $Y\sim B(n,p\cdot q)$. how about the first case ($Y\sim…
Farhad 87
- 41
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employee binomial distribution
Can anyone let me know if I am following the correct format/procedures in solving this problem and have came up with the correct answer?
If I have 80% of the employees that have their biweekly Wages deposit directly to their bank. If I select a…
Sara
- 37
2
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1 answer
binomial distribution problemo
A fair coin is tossed n times. The histogram for the resulting binomial distribution is labelled
0, 1, 2, . . . , n on the horizontal axis, and each column is 1 unit wide. How many columns are entirely contained in the interval one standard…
moon river
- 159
2
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0 answers
Average time for Minecraft wheat to grow
The Minecraft wiki says (here) that, on average, under ideal conditions, after 31 minutes and 3.14 seconds, 80% of the crops in a wheat field should be fully grown.
I tried to prove that, but my result was 34 minutes and 55.55 seconds.
I will list…
Silas
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2 answers
What is the technique for finding the probability of probability in a binomial distribution?
I know this is a tired question, but I have seen no clear answers.
I saw a related post but didn't see how it applied to the general case. In a 3b1b video, it is alluded to that given some known number of trials and successes, the probability of the…
FShrike
- 40,125
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3 answers
Median for a Binomial distribution.
Say, $X$ is the number of heads obtained in $n=10$ trials, so, $X$~$Bin(10,0.5)$.
I am a little confused in it's median.
Not in calculation, but it's meaning.
For $n=10,p=0.5$ the binomial distribution is symmetrical and Mean=Median=Mode=$5$.
Now,…
User9523
- 2,094
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2 answers
Explanation for Binomial Distribution in Statistics
In the Binomial Distribution equation for Discrete Probability Statistics, what exactly does the first part, $n!/(x!(n-x)!)$ mean for the equation, and do I have that written out correctly? And overall, what does binomial distribution do for…
T. Smith
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Binomial Distribution/probability
A rose breeder is trying to cross yellow and red roses. He finds, on average, that $1$ in every $4$ of his test seeds produce a yellow rose. If he plants $12$ seeds, determine the prob that:
Exactly $2$ roses are purely yellow.
Less than $3$ of the…
StuM
- 45
1
vote
0 answers
Probability on future days (forecasting)
I have data available for the last days. Each day my table grows by one record. I want to calculate the probability that an event occurs once in the future 7 days.
I use the binomial distribution so far, because it is only about "Yes / No" or…
Daniel
- 111
1
vote
1 answer
Determine whether a variable is Binomial
It's an exercise from the online book Bayes Rules! An Introduction to Bayesian Modeling with R.
Thus the book has no chapter with the right answers and so far I've not found a designated place to discuss its exercises, let's do the discussion…
Raibek
- 196
1
vote
1 answer
Binomial distribution probability of defective product is 0.01
Q. The probability that a product is defective is 0.01. The products are packed in boxes; each box contains 10 products. A company orders a consignment of 12 boxes of products. A purchaser randomly opens three boxes, and accepts the consignment if…
eun ji
- 51
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3 answers
In the binomial distribution, why does order not matter?
(For context): $X$ is the random variable for number of successes ($x$) out of $n$ independent trials with probability of success $p$ and probability of failure $1-p = q$
The formula for mass my book gives me for the binomial distribution is…
user865043
1
vote
1 answer
Approximately 8.33% of men are colorblind. You survey 8 men from the population of a large city and count the number who are colorblind.
This question shows up in the binomial distribution chapter in my book.
g. How many men would you have to survey in order to be at least 95%
sure you would find at least $1$ who is colorblind?
Now I know that $P(X \geq 1) = 1 - P(X=0) = 1 -…
user865043