Concept explainers
Fire Alarms A fire-detection device uses three temperature-sensitive cells acting independently of one another in such a manner that any one or more can activate the alarm. Each cell has a
a. Find the probability distribution of x.
b. Find the probability that the alarm will
c. Find the expected value and the variance for the random variable x.
a.
To find: the probability distribution for
Answer to Problem 4.108SE
Explanation of Solution
Given:
A fire detection device uses three temperature -sensitive cells.
Each cell has probability
Calculation:
Let
Therefore,
Now, to find the probability distribution for
The probability table is as follows:
Events associated | ||
Hence,the probability distribution for
b.
To find: the probability that the alarm will function when the temperature reaches
Answer to Problem 4.108SE
Explanation of Solution
Given:
A fire detection device uses three temperature -sensitive cells.
Each cell has probability
Calculation:
Let
Therefore,
Probability that the alarm will function when temperature reaches
Hence, the probability that the alarm will function when the temperature reaches
c.
To find: the expected value and the variable for the random variable
Answer to Problem 4.108SE
Explanation of Solution
Given:
A fire detection device uses three temperature -sensitive cells.
Each cell has probability
Calculation:
Let
Therefore,
Probability that the alarm will function when temperature reaches
Hence, the probability distribution for
Hence, the expected value is
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Chapter 4 Solutions
Introduction to Probability and Statistics
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