Distributions: Exercises
4. Bond Default. You hold a portfolio of 100 bonds and each has a default probability of 0.05. In this exercise, you will model default using a binomial distribution.
The binomial distribution can be used to determine the probability that some number of loans default. To calculate this probability in R, use the dbinom(k, n, p), where n is the number of bonds, k is the number of defaults, and p is the default probability for a single bond.
Calculate the probability that 3 bonds default.
# Define the number of bonds.
n <- ___
# Define the number of defaults.
k <- ___
# Define the default probability.
p <- ___
# Compute the probability of k defaults.
result <- dbinom(___, ___, ___)
# Print the result.
result
# Define the number of bonds.
n <- 100
# Define the number of defaults.
k <- 3
# Define the default probability.
p <- 0.05
# Compute the probability of k defaults.
result <- dbinom(k, n, p)
# Print the result.
result
test_error()
test_object("n", incorrect_msg="Check the number of bonds.")
test_object("k", incorrect_msg="Check the number of defaults.")
test_object("p", incorrect_msg="Check the default probability.")
success_msg("Great job!")
Remember to use
dbinom(n, k, p).