2DECISION SUPPORT TOOLANSWER 1a)A random variable is a variable that takes unknown values or functions thatassigns values to every outcome of an experiment. Discrete random variable and continuous random variables are the two types of random variables (Miller & Miller, 2015). A random variable is said to be discrete if it assumes a finite number of values or a countably infinite number of values. For example, the sum of points obtained in two throws of a fair die is a discrete random variable.A random variable is said to be continuous if it assumes uncountably infinite number of values. For example, the decay time of a radioactive particle is a continuous random variable. b)The term expected value of a random variable means the value predicted for therespective random variable. It is denoted by E(X) and serves as a measure of centraltendency of the probability distribution of X. It is usually defines as the sum of the valuesof the random variables multiplied by their respective probabilities. If X assumes thevalues x1, x2, ...., xk with respective probabilities p1, p2, ...., pk, where ∑i=1kxipi=1, then E(X)=∑i=1kxipi, provided it is finite.

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