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 = .8 of activating the alarm when the temperature reaches 100°F or higher. Let x equal the number of cells activating the alarm when the temperature reaches 100°F.

a. Find the probability distribution of x.

b. Find the probability that the alarm will function when the temperature reaches 100°F.

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