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Consider the time to recharge the flash in cell-phone
Chapter 3, Problem 137E(choose chapter or problem)
Consider the time to recharge the lash in cell-phone cameras as in Example 3-2. Assume that the probability that a camera passes the test is 0.8 and the cameras perform independently. Determine the following:
(a) Probability that the second failure occurs on the tenth camera tested.
(b) Probability that the second failure occurs in tests of four or fewer cameras.
(b) Expected number of cameras tested to obtain the third failure.
Questions & Answers
QUESTION:
Consider the time to recharge the lash in cell-phone cameras as in Example 3-2. Assume that the probability that a camera passes the test is 0.8 and the cameras perform independently. Determine the following:
(a) Probability that the second failure occurs on the tenth camera tested.
(b) Probability that the second failure occurs in tests of four or fewer cameras.
(b) Expected number of cameras tested to obtain the third failure.
ANSWER:
Solution:
Step 1 of 4:
From the example 3-2.
Given that the probability that a camera passes the test is 0.8 and the cameras perform independently.
P(camera will fail in the test) = 1 - 0.8 = 0.2
Let us denote the X = number of cameras tested until second failure occurs.
Here X is a negative binomial with p = 0.2 and r = 2.
The pmf of X is