R Exercises | Programming Exercises for Finance in the R Language

Bayesian Analysis: Exercises

1. Conditional probabilities. Let P(B) be the probability that B defaults. The following variables have been defined for you in R.

$$P(A|B) = \text{prAcondB} = 0.90$$ $$P(B) = \text{prB} = 0.10$$ $$P(A) = \text{prA} = 0.20$$

Use the variables above to compute the probabilities below:

$$P(B|A) = \text{prBcondA}$$ $$P(B \cap A) = \text{prBandA}$$



                                  prAcondB <- 0.90
                                  prB <- 0.05
                                  prA <- 0.07



                              # Compute the probability that B defaults given A.
                              prBcondA <- ___*prB/___

                              # Compute the joint probability of B and A defaulting.
                              prBandA <- prA*___

                              # Print the probabilities.
                              print(c(prBcondA, prBandA))



                                # Compute the probability that B defaults given A.
                                prBcondA <- prAcondB*prB/prA

                                # Compute the joint probability of B and A defaulting.
                                prBandA <- prA*prBcondA

                                # Print the probabilities.
                                print(c(prBcondA, prBandA))


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

Remember that P(B|A)*P(A) = P(A|B)*P(B).

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