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In: Statistics and Probability

Transistors produced by one machine have a lifetime that is exponential distributed with mean 50 hours....

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.

Solutions

Expert Solution

Answer:

Given that:

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.

orchestra answered 2 years ago
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