Probability and Statistics: Exercises
2. Approximating the normal distribution. A draw from the normal distribution can be approximated by summing draws from
uniform distributions and then subtracting the expected value. Using the function runif(n, min, max), draw 25 observations
from a uniform distribution with a minimum of 0 and a maximum of 1. Repeat this three times and then subtract the expectation, which is 1.5.
Plot a histogram of your draws using hist().
# Draw observations from uniform distribution three times.
draws_1 <- runif(___, 0, ___)
draws_2 <- ___(___, ___, 1)
draws_3 <- ___
# Sum the draws and subtract the expectation.
approx_normal_draws <- ___
# Plot histogram of observations.
___
# Draw observations from uniform distribution three times.
draws_1 <- runif(25, 0, 1)
draws_2 <- runif(25, 0, 1)
draws_3 <- runif(25, 0, 1)
# Sum the draws and subtract the expectation.
approx_normal_draws <- draws_1 + draws_2 + draws_3 - 1.5
# Plot histogram of observations.
hist(approx_normal_draws)
test_error()
test_function("runif", incorrect_msg="Did you use the `runif()` function?")
test_function("hist", incorrect_msg="Did you use `hist()` to plot a histogram?")
success_msg("Excellent work. Does your distribution appear to approximate a normal distribution well? Try increasing the number of draws.")
Did you set the parameters of the
runif() correctly?Previous Exercise Next Exercise