Binomial Distribution assignment help
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What is Binomial distribution
In probability theory and statistics, binomial distribution forms part of the wider probability distribution methods. Hence, getting to understand the probability distribution will make it simpler for us to understand binomial distribution.
A probability distribution is a mathematical function that gives the probability of occurrence of different possible outcomes in an experiment. Probability distributions are classified into discrete probability distribution and continuous probability distribution. Discrete probabilities are mainly characterized by probability mass function while continuous probability distribution has a cumulative distribution function that is continuous.
A binomial distribution, therefore, is the discrete probability distribution of the number of successes in a series of unbiased experiments. The binomial distribution is majorly used to obtain the number of successes obtained from samples that are used with replacement.
For a probability distribution to be binomial, it has to attain the following:
- It has to be based on independent experiments.
- There should be only 2 equiprobable outcomes of each experiment.
- The number of experiments should be fixed.
- The probability of success should be the same for all the experiments.
Specifications of a Binomial Distribution
Probability mass function
Probability mass function gives the number of successes that can be achieved from a particular number of experiments.
Cumulative distribution function
The CDF of a random variable, say R, evaluated at r, is the probability that R will take a value less than or equal to r.
The expectation of a binomially distributed random variable X, E[X] = np, where n is the total number of experiments conducted and p is the probability of each experiment yielding a successful result.
The variance of a binomial distribution is obtained as Var(X) = np(1-p).
Topics we cover on Binomial Distribution
Our experts have vast experience solving students’ assignment problems and therefore they have a good understanding of the most notorious topics students face in binomial distribution assignments. Listed below are some of the most frequent topics we have solved.
|Conditional binomials||The ratio of two binomial distributions|
|Bernoulli distribution||Beta distribution|
|Poisson binomial distribution||Poisson approximation|
|Normal approximation||Limiting distribution|
|Sum of binomials||Covariance between binomials|
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