Suppose that we have a shipment of components and we would like to decide if we should accept the shipment. We know that the failure time of any xeit too component has a probability density function f(t)= λe^-λt, t>0 Let our acceptance test be as follows: We choose a component from the shipment at random. If that component survives to time α, we accept the shipment (Survival to time α means that the failure time is between If the component fails before time (failure time is between α and [infinity]), we do not immediately reject the shipment. Instead, we choose another component and observe its survival time. If the AVERAGE survival time of the two samples is greater than α, we accept the shipment. Otherwise, we reject the shipment. No further samples are taken.

Required:
What is the probability of accepting the shipment?