R Exercises | Programming Exercises for Finance in the R Language

Bayesian Analysis: Exercises

2. Bayes' Theorem. Let P(B) be the probability that B defaults. The following variables have been defined for you in R.

$$P(B) = \text{prB} = 0.05$$ $$P(A) = \text{prA} = 0.10$$

Compute P(A|B) under the following two assumptions:

1. P(B|A) = 0.45.

2. A and B are independent.



                                  prB <- 0.05
                                  prA <- 0.10



                                # Compute P(A|B) if A and B are independent.
                                prBcondA0 <- ___

                                # Define P(B|A) for case where A and B are not independent.
                                prBcondA <- ___

                                # Compute P(A|B) for case where A and B are not independent.
                                prAcondB1 <- ___*prA/___



                                # Compute P(A|B) if A and B are independent.
                                prBcondA0 <- prA

                                # Define P(B|A) for case where A and B are not independent.
                                prBcondA <- 0.45

                                # Compute P(A|B) for case where A and B are not independent.
                                prAcondB1 <- prBcondA*prA/prB


                              test_error()
                              test_object("prBcondA0", incorrect_msg="Check the expression you used to compute `prBcondA0`.")
                              test_object("prBcondA", incorrect_msg="Check the expression you used to compute `prBcondA`.")
                              test_object("prAcondB1", incorrect_msg="Check the expression you used to compute `prAcondB1`.")
                              success_msg("Excellent work.")

Remember that Bayes' Theorem can be used to relate conditional and unconditional probabilities.

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