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Andrei [34K]
3 years ago
6

The lifetime of a machine part has a continuous distribution on the interval​ (0, 50​) with probability density function​ f, whe

re​ f(x) is proportional to left parenthesis 10 plus x right parenthesis Superscript negative 2. Calculate the probability that the lifetime of the machine part is less than 13.
Mathematics
1 answer:
Strike441 [17]3 years ago
4 0

Answer:

Probability that the lifetime of the machine part is less than 13 = 0.6782

Step-by-step explanation:

given that f(x)=(10+x)^{-2}

Normalizing the function we get

\int_{0 }^{50}cf(x)dx=1

\int_{0 }^{50}c(10+x)^{-2}dx=1

\therefore a=\frac{1}{\int_{0 }^{50}(10+x)^{-2}dx}

\therefore a=12

P(x< 13)=\int_{0}^{13}12(10+x)^{-2}dx\\\\P(X< 13)=0.6782

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