An appliance relies on two components, one of which has a random lifetime x_(1) and the other one has a\nrandom lifetime x_(2), where x_(1) and x_(2) are independent exponential random variables with parameters\n\\lambda and \\mu respectively. The appliance will fail when either component fails. By calculating \nt and {:x_(2)>t), show that the lifetime of the appliance also has an exponential distribution and give the\nparameter.
An appliance relies on two components, one of which has a random lifetime X and the other one has a random lifetime X2, where X and X2 are independent exponential random variables with parameters X and respectively. The appliance will fail when either component fails. By calculating P(X > t and X2 > t), show that the lifetime of the appliance also has an exponential distribution and give the parameter.