(Question II: 25 pts) An auto insurance company sent a survey for its customers.

Question

(Question II: 25 pts) An auto insurance company sent a survey for its customers. The survey consists of two questions 1) What is the current deductible on your auto insurance policy? 2) What is your car model? X: The random variable associated with the amount of deductible on an auto insurance policy (S). Y: The random variable associated with the identity of the insured car. (Y-1 for a car manufactured after 2010 and Y = 0 for a car manufactured before or during 2010). Consider the random variables X and Y have the following joint probability mass function as tabulated below. 500 1000 0.60 0.07 0.03 0.02 0.20 0.08 0 (a : 10 pts) Find the marginal PMFs (Probability Mass Functions) of X and Y

Explanation / Answer

from above below is joint probability distribution:

marginal pmf of X:

and marginal pmf of Y:

x y 0 500 1000 Total 0 0.6000 0.0700 0.0300 0.7000 1 0.0200 0.2000 0.0800 0.3000 Total 0.6200 0.2700 0.1100 1.0000

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