Problem 1

Write a function to prints out standard random normal numbers (use rnorm()) but stops (breaks) if you get a number bigger than 1.

Using next adapt the loop from last exercise so that doesn’t print negative numbers.

Problem 2

Write a function to simulate the flip a coin $n$ times, keeping track of the individual outcomes (1 = heads, 0 = tails) in a vector that you preallocte. Assume $P\left(H\right)=0.5$.

Example output:

flip_coin(10)

 [1] "H" "T" "T" "H" "H" "H" "H" "H" "T" "T"

flip_coin <- function(n){
  out <- numeric(n)
  for (i in 1:n){
    coin.out <- rbinom(1, p=0.5, n=1)
    if(coin.out==1){
      out[i] <- "H"
    } else {
      out[i] <- "T"
    }
  }
  out
}

flip_coin(10)

 [1] "T" "T" "H" "H" "H" "T" "H" "T" "T" "T"

• Modify the function so that it takes another argument, which will be the $P\left(H\right)$.

• Run the function 10, 100, 1000 and 10000 times with $P\left(H\right)=0.8$ and report the proportion of times that head is selected.

Problem 3

Write a function to calculate the median.

help:

5%%2

[1] 1

4%%2

[1] 0

Problem 4

Write a function to calculate the correlation coefficient

$$r=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2{\sum }_{i=1}^n(y_i-\overline{y}{)}^2}}$$