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    Exponential Distribution to Determine Product Lifetimes for two Products

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    A consumer is contemplating the purchase of a new compact disc player. A consumer magazine reports data on the major brands. Brand A has lifetime (TA) which is exponentially distributed with m=.02; and Brand B has lifetime (TB) which is exponentially distributed with m=.01. (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 lifetime, which one should be chosen?

    b. Find the probability that A's lifetime exceeds its expected value. Find same for B

    c. Suppose one consumer purchases a Brand A compact disc, and another consumer purchases a Brand B compact disc. Find the mean and variance of the average lifetime of the two machines and the difference between the lifetimes of the two machines.

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    Solution Preview

    Please see the attached file.

    If X ~E ( then expected value E (x)=
    Variance (X)=
    The expected life time of brand A = 1/0.02=50
    The expected life time of brand B = ...

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