A husband and wife have two cars. They can purchase special auto insurance policies for each car separately, such that each policy covers the loss only for the first accident occurred in the same year. Suppose that the numbers of accidents connected with each car are independent r.v.’s N₁,N₂ with the same distribution. The couple have also an option to buy a joint insurance for both cars which covers two accidents a year. If the premium for the joint insurance is double the premium of the individual policy, what decision should the couple make? Describe the distribution of the number of accidents which the insurance will cover for both cases and provide comparison. (Advice: Observe that these distributions are completely specified by p₀ = P(N₁ = 0) = P(N₂ = 0), and p₁ = P(N₁ = 1) = P(N₂ = 1).)