The life X in years of a voltage regulator of a car has thepdf a) What is the pr

Question

The life X in years of a voltage regulator of a car has thepdf a) What is the probability that this regulator will last atleast 7 years b) Given that it has lasted at least 7 years, what isthe conditional probability it will last at least another 3.5years? The life X in years of a voltage regulator of a car has thepdf F (x) 3x ^ 2/7 ^ 3 e^-(x/7) ^ 3 0

Explanation / Answer

Given f(x) = 3x2 / 73 * e-(x/7)^3,F(X) = int(f(x) * dx, x = 0..X) = (-e-(X/7)^3) -(-e0) = 1 - e-(X/7)^3 A) P(X >= 7) = 1 - F(7) = 1 - [1 - e-1] =e-1 = .3679 B) P(X >= 10.5 | X >= 7) = P(X >= 10.5 AND X >=7) / P(X>=7) = P(X >= 10.5) / P(X >=7) P(X >= 10.5) = 1 - F(10.5) = 1 - .9658 = .0342 P(X >= 10.5) / P(X >=7) = .0342 / .3679 = .093

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