# Tagged Questions

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### Co-occurrence Poisson binomial distribution

I'm using a Poisson binomial distribution for co-occurrence testing. I've 2 variables : X ~ Binom(px,n) and Y ~ Binom(py,n) (px and py are the probabilities, and both variable have the same number of ...
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### Help with binomial probability sample test formulation

This is a natural experiment, so I can not 'resample': My population has a property with 9 possible values: 1,2,3,9. Each value has a probability associated with it. For example 1's occur 10% but ...
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### How to calculate the binomial probability when expected frequency is a random variable

I am trying to write a simple likelihood function to calculate the binomial probability of $X$ successes from $N$ trials. The problem is that the expected proportion of successes ($p_X$) is itself a ...
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### Probabilities from Logistic Regression

I have built a logistic regression model in R and though the result appears to be satisfactory to some degree, there is one question I have not be able to address. I am not sure if my approach is at ...
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### Binomial probability problem from a book

I have a problem on binomial probability, it goes like this: A restaurant offers apple and blueberry pies and stocks an equal number of each kind of pie. Each day ten customers request pie. They ...
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### Calculating the probability of 31 of 628 items are sampled (no replacement) more than 10x amongst 150 participants drawing 50 items each

I am sorry for having to ask a simple probability question, but I have been thinking about it for weeks and an extensive google search has given no answers. I have a group of 628 questions. 31 ...
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### Modelling probabilties within friend sets

Recently, I was wondering about calculating the probability of a given individual in a given population "knowing" (let's say, present in individual's friend set) at least one person with a given trait ...
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### Binomial Conditional Probability of a an event

Determining Binomial Condition Probability of a Random Sample I have a question about binomial probability involving a conditional event. This problem keeps tripping me up, because while I know how ...
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### Standard Deviation of fixed-odds bet

I'm looking to calculate the standard deviation of a fixed-odds betting proposition. The bet pays 5/6 for a win and you lose your stake for a loss. For a bet of 100, a winner pays 83.33 (and the stake ...
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### Stochastic inequality with product of binomial distributions

I am interested in modeling the following experiment: A binomial trial with $n$ Bernoulli experiments is run. For the k positive outcomes a second (independent) binomial trial with $k$ runs with a ...
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### Binomial Events with unequal probabilities

Imagine I have a database of 1000 students. I test these students every week with questions that can be true/false. How do I rank the students according to the historical track records? The problems ...
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### How to model the probability of an event occurring on a given day when it must occur once in a set of 10 days?

I am a muslim and there is ramadan going on. The last 10 days of ramadan are really special, and in one of these 10 days there is one special night that no one knows about. The special day is more ...
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### Is it sound to take the average of a cumulative average?

Sorry, I'm a huge statistics noob. I'm looking to find the probability that a certain event occurs in a binomial experiment. I take a few thousand samples per test, and then calculate the ...
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### What is the probability of taking 15 free throws in a game and making 10 in a row? [duplicate]

What is the probability of taking 15 free throws in a game and making 10 in a row given that each shot has a 50% probability of going in? I have simulated this problem but I also want to confirm the ...
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### Distribution of independent binomial variables conditional upon the sum

Suppose that we have independent binomial variates with differing sizes and probabilities $X_i \sim Binomial(n_i,p_i)$, and $Z = \sum_iX_i$ is the sum. I understand that $Z$ is distributed ...
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### Finding the bionomial probability?

Ok so i have been taught this formula regarding binomial probability Repeat an even n times ...
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### Normal approximation to binomial

What do I do when the normal approximation is not valid? Here's the question I'm trying to answer: A student guesses all 15 answers on a multiple-choice test. There are 5 choices for each of the ...
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### Binomial probability function

What is the probability of rolling exactly two sixes in 6 rolls of a die? Solution by the Binomial Probability formula is \binom{6}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^4 = ...
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### How many measurements (10 million molecules each time) are needed to analyze 15 million unique molecues in a 20 million pool?

This is my homework: There are 20 million DNA molecules in a library for high throughput DNA sequencing, each sequencing run can generate 10 million reads (i.e., analyze 10 millions of DNA molecules), ...
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### Finding the z score and p-value of a binomial distribution

Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
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### Why doesn't this represent a normal approximation to the binomial?

Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
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### Binomial distribution where probability of success is dependent on another binomial distribution

How does one model the Binomial distribution where the probability of success is the result of another Binomial distribution. For example, say I make 10 coin tosses many times and record the number ...
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### Which test should I use?

I have a set of probabilities that an event will occur (yes/no). E.g. [0.87, 0.56, 0.97], and I need to know "What is that probability that at least X of these events occurs?". I've been looking into ...
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### 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 ...
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### Calculate a tennis players chance to win a 5set match knowing he has 50% chance of winning 1SET?

Is the following correct? My friend tells me i need to (add up the binomial probabilities of 2 wins in 2 sets, 2 wins in 3 sets and 2 wins in 4 sets THEN multiply the sum obtained by p) P(3) = 5C3 x ...
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### Best book to learn probability - Poisson, binomial, regression, etc [duplicate]

What is the best book to learn probability - Poisson, binomial, regression, etc. I am working as an odds adjuster at a bookmaker and need to advance my skills to an odds compiler level.
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### Distribution of number of Bernoulli trials given number of successes

Suppose you have a series of n trials, where the probability of success in each trial is p. The distribution of the number of successful trials follows a Binomial distribution with parameters (n, ...
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### What is the probability that a sample value from a Binomial distributions is smaller than a sample value from another?

Let $X \sim \mathrm{Binomial} (n, p_1)$ and let $Y \sim \mathrm{Binomial} (n, p_2)$ with $n, p_1$ and $p_2$ known and $p_1 < p_2$. What is the probability that a sample value $x$ drawn from $X$ is ...
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### Find the probability distribution of X? [closed]

Suppose Nokia store places 20 of its cell phones on a clearance sale, unknown to anyone 5 of these cell phones are defective. A customer selects 3 cell phones at random for inspection. Let X be the ...
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### Generating non-zero binomial probabilities (n,k ) with small p and large n - k

I am trying to generate binomial probabilities (in R) as follows: ${N \choose{k}} p^{k} (1-p)^{(n-k)}$ My problem is given $p \approx 0.03$, and $N =400$, $k>270$, I get the probability equal to ...
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### 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 ...
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### The meaning of P(X=0) in a binomial distribution

recently I was resolving an elementary problem about binomial distribution, this problem requests to determinate $P(X<=2)$, where $X$ is nonconforming products, sample is 50 units, and the fraction ...
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### Intuition behind result for binomial

We are given the following equality: $B(k;n,p)=B(k;n+1,p) + pb(k;n,p)$ where $B$ is the binomial cdf, $b$ is the binomial pdf, $n$ is the number of trials and $p$ is the probability of success. How ...
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### Probability of winning a drawing/lottery

I can't seem to get my head around this: A random drawing will be held for which there are 900 tickets sold, for which there will be one winning ticket drawn. If you purchased 25 tickets, what is the ...
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### Probability that the probability for a binomial distribution is below a certain value

This is a slightly odd problem I ran across recently. Assuming a population of size $N$ following a binomial distribution with unknown $p$, how many different samples must be taken from the population ...
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### Question related to binomial distribution

Let $X \sim Binomial (n, p)$ with both $n$ and $p$ known. Suppose for some non-increasing function $G:[0,1] \rightarrow [0,1]$, and some fixed $c_0 \in [0,1]$, we have that \begin{align} ...
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### Cumulative distribution of Binomial Random variable

How to prove this: Proposition. If $F_n$ is the distribution function of a $\textrm{Bin}(n,p)$ random variable, then, for every real fixed $t$, the sequence $\{F_n(t)\}_{n=1}^\infty$ is ...
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### How to compute the number of games that must be played for the better team to win 70% of the time?

I've been stuck on this sample statistics problem for a couple days now: Assume that two baseball teams have win records of $58\%$ and $54\%$. Demonstrate how to compute or estimate the number of ...
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### What is the distribution for modeling the number of successes in a specific order in N trials?

The Binomial distribution models the number of successes in N trials, but the successes can be in any order. What's the distribution for when the successes have to be in a specific order? Do you just ...
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### Probability over multiple blocks of events

I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any ...
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### Error count limit for known residual failure rate and desired false-positive rate?

We perform a known fixed number $K$ of independent experiments, each of which has known/assumed residual odds $p$ to fail. We count the number $N$ of failures. How can I choose $M$ so that $N>M$ ...
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### probability of the next number of events occurring when the true probability is known [duplicate]

Possible Duplicate: Probability of getting between What is the probability that at least 24 of the next 50 people like to swim when the true probability of people liking to swim is 35%? I ...
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### How to determine larger probability of drawing one element from a set when set size and number of draws with replacement vary?

Which is the better scenario in terms of probability with the following: Scenario 1 I have a hat with 5 tickets in it (I have one). There is one single draw. I have a 20% chance that my ticket is ...
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### 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 ...
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### Estimating variability of unseen factor

I'm looking at binomial data where I believe that the probability of the outcome is the product of two independent factors. If you think of it as a two step decision, At the first step, there is a ...
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### Binomial Probability Question

Given two basketball players. John made 38/50 free throws. Mike made 80/100 free throws. What is probability that Mike is better at free throws than John?
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### Normal distribution and weight of babies problem

X is the weight of a baby when born (in gram). If the distribution of X is N(3315, 575) and Y is the number of babies with weight lower than 2719 in a random sample of 25, then P[Y≤4] is about...? ...
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### Probability of getting between

...2 to 5 questions answered correctly, out of 20 of them? Each question has 5 choices. Probability of getting one right is 1/5. Probability of getting exactly 1 right is ${20 \choose 1} p^1 q^{19}$, ...
There are 100 people in a room. What are the odds at least 1 person is born in January? What is the best way to calculate this? I used Binomial Distribution. $E(x) = np = 100 \frac{1}{12} = 8.3$ ...