where I X ( x i ) {\displaystyle I_{X}(x_{i})} is the self-information associated with particular outcome; I X {\displaystyle I_{X}} is the self-information of the random variable X {\displaystyle X} in general, treated as a new derived random variable; and E ⁡ [ I X ] {\displaystyle \operatorname {E} [I_{X}]} is the expected value of this new random variable, equal to the sum of the self-information of each outcome, weighted by the probability of each outcome occurring[3]; and b {\displaystyle b} , the base of the logarithm, is a new parameter that can be set different ways to determine the choice of units for information entropy.