# Discrete Random Variables (DRV)

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(X2) -[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) = a2Var(X), where a and b are constants
• Var(aX± bY) = a2Var(X)+b2Var(X) , where a and b are constants, X and Y are independent
• standard deviation = √(Var(X))

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