The lifetime, in years, of a certain type of electrical switch has an exponential distribution with an average lifetime of 2 years. Question. For a single system, what is the probability we can keep one switching mechanism operable for 10 years if we assume we can replace a switch due to failures up to three times during the 10-year period?

The lifetime, in years, of a certain type of electrical switch has an exponential distribution with an average lifetime of 2 years. Question. For a single system, what is the probability we can keep one switching mechanism operable for 10 years if we assume we can replace a switch due to failures up to three times during the 10-year period?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

The lifetime (in years) of a specific helicopter part follows an exponential distribution whoseexpectation is 4 years.(a) What is the probability that one of these parts will stay operational for more than 4.4 years?(b) What is the probability that one of these parts will stay operational between 2.5 and 4 years.
This is an econometrics question please help me solve it.
In a certain year, the percent of persons (ages five and older) in each state who speak a language at home other than English was approximately exponentially distributed with a mean of 9.352. Suppose we randomly pick a state. Find the probability that the percent is between 6 and 17. (Round your answer to four decimal places.)
The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 7 minutes. What is the probability that a car can complete the transaction in less than 4 minutes? Probability =
The time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee. If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?
Q3.25
Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. Risk Age SystolicBloodPressure Smoker 11 58 152 Yes 24 65 163 No 13 58 155 No 56 86 177 Yes 27 59 196 Yes 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 38 59 209 Yes (a) Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, systolic blood pressure, and whether the person is a…
In a certain year, the percent of persons (ages five and older) in each state who speak a language at home other than English was approximately exponentially distributed with a mean of 9.352. Suppose we randomly pick a state. Find the probability that the percent is less than 11. (Round your answer to four decimal places.)
The average lifetime of a certain new cell phone is 5 years. The manufacturer will replace any cell phone failing within 3 years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.What is the median lifetime of these phones (in years)? (Round your answer to four decimal places.)