Finite Math Examples

$\begin{array}{c} x & P (x) \\ 1 & - 13 \\ 2 & - 31 \\ 3 & - 59 \\ 4 & - 97 \\ 5 & - 146 \end{array}$

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

$- 13$ is not greater than or equal to $0$ , which doesn't meet the first property of the probability distribution.

$- 13$ is not greater than or equal to $0$

Step 3

$- 31$ is not greater than or equal to $0$ , which doesn't meet the first property of the probability distribution.

$- 31$ is not greater than or equal to $0$

Step 4

$- 59$ is not greater than or equal to $0$ , which doesn't meet the first property of the probability distribution.

$- 59$ is not greater than or equal to $0$

Step 5

$- 97$ is not greater than or equal to $0$ , which doesn't meet the first property of the probability distribution.

$- 97$ is not greater than or equal to $0$

Step 6

$- 146$ is not greater than or equal to $0$ , which doesn't meet the first property of the probability distribution.

$- 146$ is not greater than or equal to $0$

Step 7

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