
  # define a function for the estimator
           
           
  # repeatedly compute estimates and store the results in est_biased
  set.seed(123)
           
           
  # plot a histogram of est_biased
           
           
  # add a red vertical line at mu = 10


           # define a function for the estimator
           Y_tilde <- function(x){sum(x)/(length(x)-1)}
           
           # repeatedly compute estimates and store the results in est_biased
           set.seed(123)
           est_biased <- replicate(n = 10000, expr = Y_tilde(rnorm(5, 10, 5)))
           
           # plot a histogram of est_biased
           hist(est_biased)
           
           # add a red vertical line at mu = 10
           abline(v = 10, col = "red")


           test_function_definition("Y_tilde", function_test = {
           test_expression_result("Y_tilde(1:10)")
           test_expression_result("Y_tilde(1:25)")
           test_expression_result("Y_tilde(seq(0, 1, 0.1))")
           })
           test_object("est_biased")
           test_function("hist", args = "x")
           test_function("abline", args = c("v", "col"))