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 temperature reaches 100_Fahrenheit or higher. Let X equal the number of cells activating the alarm when the temperature reaches 100_Fahrenheit
(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.