ABSTRACT
This chapter introduces the concept of a random variable and studies discrete distributions in detail. Discrete random variables are whose range is finite or countable. In particular, it means that their values can be listed, or arranged in a sequence. Examples include the number of jobs submitted to a printer, the number of errors, the number of error-free modules, the number of failed components, and so on. On the contrary, continuous random variables assume a whole interval of values. Examples of continuous variables include various times, also physical variables like weight, height, voltage, temperature, distance, and the number of miles per gallon. In general, the joint distribution cannot be computed from marginal distributions because they carry no information about interrelations between random variables. Chebyshev’s inequality shows that in general, higher variance implies higher probabilities of large deviations, and this increases the risk for a random variable to take values far from its expectation.
