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juliabinomial-coefficients

Binomial Experiment

How do I use the Binomial function to solve this experiment:

 number of trials -> n=18, 
 p=10%  
 success x=2

The answer is 28% . I am using Binomial(18, 0.1) but how I pass the n=2?

julia> d=Binomial(18,0.1)
Binomial{Float64}(n=18, p=0.1)
pdf(d,2)

How can I solve this in Julia?

Solution

  • What you want is the Probability Mass Function, aka the probability, that in a binomial experiment of n Bernoulli independent trials with a probability p of success on each individual trial, we obtain exactly x successes. The way to answer this question in Julia is, using the Distribution package, to first create the "distribution" object with parameters n and p, and then call the function pdf to this object and the variable x:

    using Distributions

n = 18  # number of trials in our experiments
p = 0.1 # probability of success of a single trial
x = 2   # number of successes for which we want to compute the probability/PMF

binomialDistribution = Binomial(n,p)

probOfTwoSuccesses = pdf(binomialDistribution,x)

    Note that all the other probability related functions (like cdf, quantile, .. but also rand) work in the same way.. you first build the distribution object, that embed the specific distribution parameters, and then you call the function over the distribution object and the variable you are looking for, e.g. quantile(binomialDistribution,0.9) for 90% quantile.