Transistors produced by one machine have a lifetime that is exponential distributed with mean 50 hours. Those produced by another machine have a lifetime that is exponential distributed with mean 100 hours. A package of transistors contains 3 produced by the first machine and 9 produced by the second machine. Let X be the lifetime of a transistor picked at random from this package.
Find: (a) the cdf of X; (b) P(X > 150); (c) the pdf of X; (d) E[X]; (e) Var(X); (f) Is X memoryless? Either give a proof or counterexample.