Answer:
(a) The probability that the lifetime is at most 2000 h is 0.8647.
(b) The probability that the lifetime is at most 2000 h is 0.8647.
(c) The probability that the lifetime is between 500 h and 2000 h is 0.4712.
(d) The variance of the lifetime of a particular component is 10⁻⁶.
Step-by-step explanation:
Let <em>X </em>= lifetime of a particular component
The random variable
The probability distribution function of an exponential distribution is:
(a)
Compute the probability that the lifetime is at most 2000 h as follows:
Thus, the probability that the lifetime is at most 2000 h is 0.8647.
(b)
Compute the probability that the lifetime is more than 1000 h as follows:
Thus, the probability that the lifetime is more than 1000 h is 0.3679.
(c)
Compute the probability that the lifetime is between 500 h and 2000 h as follows:
Thus, the probability that the lifetime is between 500 h and 2000 h is 0.4712.
(d)
The variance of an exponential distribution is,
The variance of the lifetime of a particular component is:
Thus, the variance of the lifetime of a particular component is 10⁻⁶.