6. The Always Ready Battery Co. has developed a new

"Failsafe" battery that incorporates a small secondary battery that becomes immediately functional upon failure of the main battery. The operating life of the main battery is a Gamma-distributed random variable as Xl ~

Gamma(3,1), where Xl is measured in years. The operating life of the secondary battery is also Gamma distributed as X2 ~ Gamma(2, 1). The operating lives of the main and secondary batteries are independent.