4.111 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 probability p=0.8 of activating the alarm when the tempera- ture reaches 38C or higher. Let x equal the number of cells activating the alarm when the temperature reaches 38C.

a. Find the probability distribution of x.

b. Find the probability that the alarm will function when the temperature reaches 38C.

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