Finite Math Examples

$\begin{array}{c} x & P (x) \\ 1 & 8 \\ 2 & 13 \\ 3 & 18 \\ 10 & x \\ 100 & x \end{array}$

Step 1

A discrete random variable $x$ takes a set of separate values (such as $0$ , $1$ , $2$ ...). Its probability distribution assigns a probability $P (x)$ to each possible value $x$ . For each $x$ , the probability $P (x)$ falls between $0$ and $1$ inclusive and the sum of the probabilities for all the possible $x$ values equals to $1$ .

1. For each $x$ , $0 \leq P (x) \leq 1$ .

2. $P (x_{0}) + P (x_{1}) + P (x_{2}) + \dots + P (x_{n}) = 1$ .

Step 2

$8$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$8$ is not less than or equal to $1$

Step 3

$13$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$13$ is not less than or equal to $1$

Step 4

$18$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$18$ is not less than or equal to $1$

Step 5

$x$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$x$ is not less than or equal to $1$

Step 6

The probability $P (x)$ does not fall between $0$ and $1$ inclusive for all $x$ values, which does not meet the first property of the probability distribution.

The table does not satisfy the two properties of a probability distribution