Question

The life of one Tx-991 component has an exponential distribution with average of 2 years. It is considered that a Tx-991 component is defective if it stops working within 1 year. Fifty Tx-991 components are tested, and its noticed that they fail independently. How many of these components are expected to be defective?

Answer 1

Solution :

Let X be a random variable which represents the average life of Tx-991 component.

Given that, X follows exponential distribution with mean of 2 years.

Probability density function of an exponentially distributed random variable with mean λ is given by,

We have, λ = 2 years

Hence, probability density function of X would be given by,

A Tx-991 component is said to be defective if it fails within one year. Hence, first of all we shall find the what percentage of all Tx-991 components fail within one year.

i.e. We need to obtain P(X < 1).

0.39347 = 39.347%

Hence, 39.347% of all Tx-991 components fail within one year.

Number of tested components = 50

39.347% of 50 = 50×39.347/100 = 19.6735

On rounding to nearest whole number we get,

39.347% of 50 = 20

Hence, 20 components are expected to be defective.

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