A discrete random variable is one that takes discrete value e.g. 1, 2.4, 3, etc. For example, if a discrete random variable, X, represents the number shown on a dice, then X can only take 1, 2, 3, 4, 5 and 6.

This is in contrast to continuous random variables. If we have a continuous variable, Y, where 0<Y<3, then the values that Y can take is infinite, as long as Y is take any value between 0 and 3.

**Formulae for discrete random variables**

- Expected value of X = E(X) = ΣxP(X=x)
- variance of X = Var(X) = E(X
^{2}) -[E(x)]^{2} - E(aX± b) = aE(X) + b,
*where a and b are constants* - E(aX± b) = aE(X) + bE(Y), ,
*where a and b are constants*, X and Y are independent - Var(aX± b) = a
^{2}Var(X),*where a and b are constants* - Var(aX± bY) = a
^{2}Var(X)+b^{2}Var(X) ,*where a and b are constants*, X and Y are independent - standard deviation = √(Var(X))

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