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 - the smallest suitable number
Each year, a detailed study is conducted on a random sample of 36 Lorenz birdwing butterflies in Town A. A Lorenz birdwing butterfly is considered to be very large if its wingspan is greater than 17.5 cm. The probability that the wingspan of any…
Ning
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Fitting a truncated binomial distribution
I have some data that I want to try fit a binomial distribution to. However, all the data for zero values is missing due to the data collection method.
Is there a function in R or MATLAB that can fit truncated binomial distributions?
For…
J.M
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2 answers
How do I apply the binomial distribution formula
How do I apply the binomial distribution formula for the following problem?
Assume that 15% of the population is allergic to cats. If you randomly select 60 people for a medical trial, what is the probability that 7 of those people are allergic to…
sg2019
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2 answers
Needs clarity with notations
I am reading a paper and it has a bit of mathematical notation that I need help with. I don't have a mathematics background therefore, I would really appreciate it if someone can help me with it. The formula is :
Can someone explain what ';' means…
John
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Getting at least 1 red queen after 5 draws from standard deck with replacement
If 5 cards are randomly selected from a standard deck of cards with replacement, what's the probability of getting at least 1 red queen?
Here's what I've done but I'm unsure if it's right, here I'm assuming this is a binomial distribution:
$$Y\sim…
user672518
- 97
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Binomial Probability; Known overall success rate, need to find a weighted p value
I have a weighted coin with an unknown $p$ value and some success/failure criteria.
An experiment consists of:
$\text{Pr}($heads$)$ = $p$, $\text{Pr}($tails $)$= $(1 - p)$
The success event is having $3$ heads with less than $4$ tails
The failure…
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How to find the probability that $|X-Y|=0$?
So I have $X$, a $Bin(5,0.5)$ variable and $Y$, a $Bin(7,0.5)$ variable. I have to find $P[|X-Y|=0]$.
According to my understanding, this probability is equivalent to $P[X=Y]$,
which is equal to
$$\sum\limits_{k=0}^5 P[X=k,Y=k]$$
I took the upper…
AP _
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Binomial distribution Bp,n , where p≠0 , has the same mean and standard
A Binomial distribution Bp,n , where p≠0 , has the same mean and standard deviation, namely μ=σ .
Find the mean of Bp,n+1 .
Atul
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Expectation of the inverse of Binomial distribution
Suppose the random variable $X_i$ are i.i.d and follow $Binomial(N,p)$.
Then, can we compute the following expectation?
$E\big[\frac{1}{a+X}\big]$ where $a>0$.
user3509199
- 175
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Binomial distribution and hypothesis test.
Sign test: A new experimental drug is given to patients suffering from
severe migraine headaches. Patients report their pain experience on a scale of
1 – 10 before and after the drug. The difference of their pain measurement
is recorded. If…
ThrmsNPrfs
- 129
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2 answers
Binomial Distribution of Random Variable
The mean of defective blades supplied in packets of $10$ is $1$. in how many packets of this make out of $1000$ packages would you expect to find at least $4$ non defective blades.
Answer given in my book is $13$ whereas me and my friends are…
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Binomial Distribution: How to know the values of n, p and x from a worded problem?
The Problem:
A tour operator organises a trip to Las Vegas. The tour operator knows that the probability of people withdrawing is 0.08 (independent event) so accepts 22 bookings even though only 20 tickets are available. What is the probability he…
Karan Bal
- 13
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1 answer
PMF of X~Binomial Coin Toss
Doing some practice problems from "Introduction to Probability" (Blitstein)
There are two coins, one with probability p1 of Heads and the other with probability p2 of Heads. One of the coins is randomly chosen (with equal probabilities for the two…
user603569
- 175
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Number of trials follows the binomial distribution
Two random variables follow the following Binomial distribution.
$N_i\sim B(S_i,\delta)$, $H_i \sim B(N_i,\alpha)$, where $\alpha$ is not a function of $\delta$.
These two random variables are related in a sense that in each period i, $N_i$ is…
user3509199
- 175
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1 answer
Why is a portion of the expected value for a binomial random variable equal to 1?
Trying to follow a proof for the expected value of a binomial random variable equal to np. I'm stumped on this step:
why does
$$\sum_{j=0}^m\binom{m}{j}p^j(1-p)^{m-j}$$
result in 1?
juanchito
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