A consumer is contemplating the purchase of a new smart phone. A consumer magazine reports data on the major brands. Brand A has lifetime (TA), which is exponentially distributed with m = 0.2; and Brand B has lifetime (TB), which is exponentially distributed with m = 0.1. (The unit of time is one year.)
a. Find the expected lifetimes for A and B. If a consumer must choose between the two on the basis of maximizing expected life-time, which one should be chosen?
b. Find the probability that A’s lifetime exceeds its expected value. Do the same for B. What do you conclude?
c. Suppose one consumer purchases Brand A, and another consumer purchases Brand B. Find the mean and variance of (i) the average lifetime of the two devices and (ii) the difference between their lifetimes.