A particular model of an HDTV is manufactured in three different plants, A, B, a

Question

A particular model of an HDTV is manufactured in three different plants, A, B, and C, of the same company. Because the workers at A, B, and C are not equally experienced, the quality of the units differs from plant to plant. The pdf's of the time-to-failure X, in years, are where u (x) is the unit step. Plant A produces there times as many units as B, which produces twice as many as C. The TVs are all sent to a central warehouse, intermingled, and shipped to retail stores all around the country. What is the expected lifetime of a unit purchased at random?

Explanation / Answer

Use the following rules for combining independent normal variables A and B. Mean(n*A) = n*Mean(A) Mean(A + B) = Mean(A) + Mean(B) Mean(A - B) = Mean(A) - Mean(B) Varaince(n*A) = (n^2)*Var(A) Variance(A + B) = Var(A) + Var(B) Variance(A - B) = Var(A) + Var(B) The plus sign in the last line is NOT an error. You ALWAYS add variances, which I presume you know is the square of standard deviation. Start part (a) with E(X - Y) = E(X) - E(Y) = 1 - 2 = -1 Var(X - Y) = Var(X) + Var(Y) = 1 + 4 = 5

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