Finite Math Examples

\begin{matrix} x & P (x) 10 & 1 20 & 2 30 & 3 40 & 4 \end{matrix}

$\begin{array}{c} x & P (x) \\ 10 & 1 \\ 20 & 2 \\ 30 & 3 \\ 40 & 4 \end{array}$

Step 1

A discrete random variable

x

$x$ takes a set of separate values (such as

0

$0$ ,

1

$1$ ,

2

$2$ ...). Its probability distribution assigns a probability

P (x)

$P (x)$ to each possible value

x

$x$ . For each

x

$x$ , the probability

P (x)

$P (x)$ falls between

0

$0$ and

1

$1$ inclusive and the sum of the probabilities for all the possible

x

$x$ values equals to

1

$1$ .

1. For each

x

$x$ ,

0 \leq P (x) \leq 1

$0 \leq P (x) \leq 1$ .

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

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

Step 2

1

$1$ is between

0

$0$ and

1

$1$ inclusive, which meets the first property of the probability distribution.

1

$1$ is between

0

$0$ and

1

$1$ inclusive

Step 3

2

$2$ is not less than or equal to

1

$1$ , which doesn't meet the first property of the probability distribution.

2

$2$ is not less than or equal to

1

$1$

Step 4

3

$3$ is not less than or equal to

1

$1$ , which doesn't meet the first property of the probability distribution.

3

$3$ is not less than or equal to

1

$1$

Step 5

4

$4$ is not less than or equal to

1

$1$ , which doesn't meet the first property of the probability distribution.

4

$4$ is not less than or equal to

1

$1$

Step 6

The probability

P (x)

$P (x)$ does not fall between

0

$0$ and

1

$1$ inclusive for all

x

$x$ values, which does not meet the first property of the probability distribution.

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