Suppose that the lifetime of a particular component has an exponential distribution with mean value 1000h.

(a) What is the probability that the lifetime is at most 2000h?
(b) What is the probability that the lifetime is more than 1000h?
(c) What is the probability that the lifetime is between 500h and 2000h?
(d) Compute the variance of the distribution?

(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 X = 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.

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

x = 23.78

step-by-step explanation: