a. What is a random variable?
b. What is a probability distribution?
c. An insurance association's study of home smoke detector use involves homes randomly selected in groups of 4. The accompanying table lists values and probabilities for x, the number of homes (in groups of 4) that have smoke detectors installed (based on data from the National Fire Protection Association). Does this table describe a probability distribution? Why or why not?
d. Assuming that the accompanying table does describe a probability distribution, find its mean.
e. Assuming that the accompanying table does describe a probability distribution, find its standard deviation.

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P(x) 0.0004 0.0094 0.0870 0.3562 0.5470