As mentioned in the previous section, in this course we will only work with discrete random variables that can take a finite amount of values. This means that X can be one of the values [math]x_1,x_2x_3,...,x_n[/math][br][br]For any random variable, there is a corresponding probability distribution which describes the probability that the variable will take a particular value.[br][br]The probability that the variable X takes value x is written as P(X = x).[br][br]If X is a random variable with possible values [math]\left\{x_1,x_2,x_3,...,x_n\right\}[/math] and corresponding probabilities [math]\left\{p_1,p_2,p_3,...,p_n\right\}[/math] such that [math]P\left(X=x_i\right)=p_i[/math], [math]i=1,...n[/math], then:[br][list][*][math]0\le p_i\le1[/math] for all [math]i=1,...,n[/math][br][math]\sum^n_{i=1}\left(p_i\right)=p_1+p_2+p_3+...+p_n=1[/math][br][math]\left\{p_1,p_2,p_3,...,p_n\right\}[/math] describes the [b]probability distribution[/b] of X.[br][br][/*][/list]

Suppose X is the number of heads obtained when 2 coins are tossed. The possible values for X are {0, 1, 2}, with corresponding probabilities [math]\left\{\frac{1}{4},\frac{1}{2},\frac{1}{4}\right\}[/math]. See that all the probabilities are between 0 and 1 and that they add up to 1.