Solutions to the MCS tutorial exercises

#MCS-Tutorial exercises

Solutions to the exercises that are mentioned in the tutorial on Monte Carlo Simulations.

ex_1.R

# 1. Write a for-loop that loops over the vector `c(1,2,3,4,5)` and computes the 
#  square root for each element.
input_vector <- c(1, 2, 3, 4, 5)

output_container <- rep(NA, length(input_vector))

for (i in seq_along(input_vector)){
  square_root <- sqrt(input_vector[i])
  output_container[i] <- square_root
}
output_container

ex_2.R

# 2. Write a for loop that draws 10 numbers from a normal distribution with
#  mean `0` and standard deviation `1`.
output_container <- rep(NA, 10)

for (i in seq_len(10)){
  random_number <- rnorm(1)
  output_container[i] <- random_number
}
output_container

# Note: the same could be accomplished without a loop via: rnorm(10)

ex_3.R

# 3. Write a for-loop that loops over the columns of the tibble 'ex_tib', and 
#  computes the median of the elements in each column:

ex_tib <- tibble::tibble(
  "a" = rnorm(5, mean = 5, sd = 2),
  "b" = rpois(5, lambda = 3),
  "c" = rcauchy(5, location = 3, scale = 2)
)

output_container <- rep(NA, ncol(ex_tib))

for (i in seq_along(ex_tib)){
  col_median <- median(ex_tib[[i]])
  output_container[i] <- col_median
}
output_container

ex_4.R

# 4. Compute the square root for each element of the vector `c(1,2,3,4,5)` 
#  by using a map-function from `purrr`. In the first case, your solution 
#  should  take the form of a list, in the second case an atomic vector of 
#  type `character`.
purrr::map(.x = c(1,2,3,4,5), .f = sqrt) # Results in a list
purrr::map_chr(.x = c(1,2,3,4,5), .f = sqrt) # Results in a character vector

ex_5.R

# 5. Draw 10 numbers from a normal distribution with mean `2` and standard 
#  deviation `4`. Again, use a map-function from `purrr´ and return the result 
#  one time as an atomic vector of type `double` and one time of type `character`.
purrr::map_dbl(.x = 1:10, .f = ~rnorm(n = 1, mean = 2, sd = 4)) # Results in a double vector
purrr::map_chr(.x = 1:10, .f = ~rnorm(n = 1, mean = 2, sd = 4)) # Results in a character vector

ex_6.R

# 6. Computes the median of the elements in each column of the tibble `ex_tib` 
#  as defined above. The result should come in form of a `list`.
ex_tib <- tibble::tibble(
  "a" = rnorm(5, mean = 5, sd = 2),
  "b" = rpois(5, lambda = 3),
  "c" = rcauchy(5, location = 3, scale = 2)
)

purrr::map(.x = ex_tib, .f = median)