In Example 6.8, we introduced the concept of a censored experiment in which n components are put on test and the experiment terminates as soon as r of the components have failed. Suppose component lifetimes are independent, each having an exponential distribution with parameter λ. Let Y1, denote the time at which the first failure occurs, Y2 the time at which the second failure occurs, and so on, so that Tr = Y1 + ⋯ + Yr + (n − r)Yr is the total accumulated lifetime at termination. Then it can be shown that 2λTr has a chi-squared distribution with 2r df. Use this fact to develop a 100(1 − α)% CI formula for true average lifetime 1/λ. Compute a 95% CI from the data in Example 6.8.
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Chapter 7 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forward2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forward
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