d) You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies $P(T ge t) = e^{-frac{t}{5}}, t > 0$ I purchase the product and use it for two years without any problems. What is the probability that it breaks down in the third year?
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This is equal to P(2 < T ≤ 3) = P(T ≤ 3) - P(T ≤ 2). Using the given equation, we have P(T ≤ 3) = e^(-3/5) and P(T ≤ 2) = e^(-2/5). Therefore, P(2 < T ≤ 3) = e^(-3/5) - e^(-2/5). ** Show more…
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