Questions tagged [binomial-distribution]

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)

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Cumulative Multinomial Distribution does not seem to add up to 1.00 for parameters >3

For a multinomial distribution $P = ( n! / (\prod_{i=1}^k {n_i!}) ) * ( \prod_{i=1}^k {{p_i}^{n_i}})$ If you sum the resulting multinomial distribution for every possible unique frequency for k=2 for ...
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Upper Bound on the Probability of the Difference of Binomial Distributions

We start by defining a binomial difference distribution Let $X\sim \text{Bin}(n, p)$, $Y\sim \text{Bin}(n, q)$, $Z=X-Y$ I've found out that this distribution is somewhat difficult to write down ...
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How would I use a normal distribution approximation to perform a hypothesis test? [closed]

A company produces wine glasses in large quantities. It is known from previous records that 1% of the glasses have a hairline fracture. In a separate experiment, a random sample of 300 glasses were ...
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Distribution of $\sqrt{npq}(X-np)$ for large n where $X$ has a binomial distribution with parameters $n,p$ and $q=1-p$

Question: Let $X$ be a binomial random variable with parameters $n,p$. Let $q=1-p$. What is the limiting distribution of $a(X+b)$ for large $n$, where $a=\sqrt{npq}$ and $b=-np$? My attempt: The ...
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Central Limit Theorem - Asymptotic approximation to sums of Poisson random variables and Binomial random variables

Question: Let $X_1, X_2, ...$ be a sequence of iid $\textrm{Poi}(5)$ variables. Let $Y_1, Y_2, ...$ be a sequence of iid $\textrm{Bin}(10,\dfrac{1}{2})$ variables. Define the sums $S_n = \sum_1^n X_i$ ...
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