what is a probability function ?

Probability Function :

Probability function: A function defined as

\[f\left(x\right)=P\left(X=x\right)\]

is called probability function of a random variable if it satisfies the following properties

(i) \[f\left(x\right)>0\]

(ii) \[\sum f\left(x\right)=1\]

Example 1:

Show that the following function is a probability function

Answer:

All the values of f(x) >=0 So (i) property of probability function is satisfied.

Also 1/36+3/36+5/36+7/36+9/36+11/36 = 36/36 =1

i.e (ii) property of probability function is satisfied.

Hence f(x) is a probability function.