# A-level Mathematics/MEI/S1/Discrete Random Variables

< A-level Mathematics‎ | MEI‎ | S1

## Discrete Random Variables

Discrete random variables are the models for the probabilities of particular results. They are represented by the notation, ${\displaystyle P(X=R)}$ (Where P is the probability of the Discrete Random Variable, X , taking on the result, R.). A discrete random variable can only take on the values r1,r2,r3...rn with the probabilities p1, p2, p3...pn respectively. Discrete random variables allow us to produce a Discrete Frequency Distribution. Discrete meaning that the value of the results can only take on positive whole integers. In S1, Discrete distributions are limited to a finite number of outcomes.

## Exemplar Question

Questions often involve working with algebra in order to find the probabilities, in OCR(MEI), you will often have to work out the value of k in order to work out the probabilities.

The probability distribution of a discrete random variable, X, is given by

${\displaystyle P(X=R)={\frac {kr}{8}}R=2,4,6,8.}$


Find the value of k and tabulate the probability distribution.

To find the value of k, we need to tabulate our probabilities and substitute the values of R into the discrete random variable, X.

    R || 2 | 4 | 6 | 8 ||
p(x=R)|| ${\displaystyle {\frac {k2}{8}}}$