unit_02_exercise_1_handout.Rmd

# Ii to generate textttoutcometest the textttsample

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ii. To generate \texttt{outcome.test}, the \texttt{sample()} command draws from the values \texttt{0} and \texttt{1} with probabilities corresponding to those specified by \texttt{prob}. Which number corresponds to heads, and which corresponds to tails? \vspace{2.5cm} iii. Why is it important to sample with replacement? \vspace{3cm} b) The following code uses a \texttt{for} loop to repeat the experiment and record the results for the number of times specified by \texttt{number.replicates}. The term \texttt{k} is an index, used to keep track of each iteration of the loop; think of it as being similar to the *k* (or *i*) in sigma notation. The \texttt{vector()} function creates an empty vector with length \texttt{number.tosses} that is filled with \texttt{0}; later on, the results will be recorded in this vector, \texttt{number.heads.per.replicate}. {r simulateCoinTossing, eval = FALSE} #set the parameters prob.heads = 0.7 number.tosses = 10 number.replicates = 50 number.heads.per.replicate = vector("numeric", number.tosses) #set the seed set.seed(2014) #simulate the coin tosses for(k in 1:number.replicates){ outcome.replicate = sample(c(0,1), size = number.tosses, prob = c(1 - prob.heads, prob.heads), replace = TRUE) number.heads.per.replicate[k] = sum(outcome.replicate)

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} #view the results number.heads.per.replicate addmargins(table(number.heads.per.replicate)) #calculate the probability greater.than.5 = (number.heads.per.replicate > 5) table(greater.than.5)  i. The parameters of the experiment have already been filled in, with the probability of heads being 0.7 and the number of tosses set to 10. This code repeats the experiment 50 times, as specified by \texttt{number.replicates}. Run the code chunk. ii. How many heads were observed in the fourth replicate of the experiment? Hint: look at \texttt{number.heads.replicate}. \vspace{2cm} iii. Out of the 50 replicates, how often were 10 heads observed in a single experiment? \vspace{2cm} iv. From the displayed results of the simulation, calculate an estimate of the probability of observing 6 or more heads when a coin is tossed 10 times. \vspace{4cm}
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