R Solutions

#. Imagine rolling a fair, six-sided die, and then flipping a fair, two-sided coin the number of times specified with the die (i.e., if we roll a 3, flip the coin 3 times). Let X be the number of heads you get in this experiment. Use a simulation in R to estimate the mean, median and mode of X.

#replicate
set.seed(110)
sims = 1000

#keep track of X
X = rep(0, sims)


#run the loop
for(i in 1:sims){

  #generate a roll
  roll = sample(1:6, 1)

  #flip the coin the specified number of times
  for(j in 1:roll){

    #flip the coin
    #recall that 'runif(1)' draws a random value between 0 and 1, so
    #   count 'heads' as getting a value below 1/2
    flip = runif(1)

    #see if we got heads; increment if we did
    if(flip <= 1/2){
      X[i] = X[i] + 1
    }
  }
}

#find the mean and median
mean(X); median(X)

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