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r - Tossing 3 fair coins in R

问题描述

X = # of heads showing when three coins are tossed.
Find P(X=1), and E(X).

Say, I want to solve this problem using sample(), and replicate() functions in R even though there is a function called rbinom().

My attempt:

noOfCoinTosses = 3;
noOfExperiments = 5;
mySamples <-replicate(noOfExperiments,
                    {mySamples <- sample(c("H", "T"), noOfCoinTosses, replace = T, prob=c(0.5, 0.5))
                    })
headCount = length(which(mySamples=="H"))
probOfCoinToss <- headCount / noOfExperiments   # 1.6
meanOfCoinToss = ??

Am I on a right track regarding the P(X)? If yes, how can I find E(X)?

标签： rprobability

解决方案

The results in mySamples stores the experiments per column, so you'll have to count the occurrence of head per column. The probability is then the frequency / nr of experiments, while the mean in this case is the frequency:

noOfCoinTosses = 3;
noOfExperiments = 5;
mySamples <-replicate(noOfExperiments,
                      {mySamples <- sample(c("H", "T"), noOfCoinTosses, replace = T, prob=c(0.5, 0.5))
                      })
headCount <- apply(mySamples,2, function(x) length(which(x=="H")))
probOfCoinToss <- length(which(headCount==1)) / noOfExperiments   # 1.6
meanOfCoinToss <- length(which(headCount==1))

When you want to calculate a real mean, you can put this into a function and replicate that n times. Then the mean will become the average of the replicated meanOfCoinToss

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