32. Fire Alarms A fire-detection device uses three temperature-sensitive cells acting independently of one another so that

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32. Fire Alarms A fire-detection device uses three temperature-sensitive cells acting independently of one another so that any one or more can activate the alarm.

Each cell has a probability p5.8 of activating the alarm when the temperature reaches 578C or higher. Let x equal the number of cells activating the alarm when the temperature reaches 578C.

a. Find the probability distribution of x.

b. Find the probability that the alarm will function when the temperature reaches 578C.

c. Find the expected value and the variance for the random variable x.

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