Finite Math Examples

$\begin{array}{c} x & P (x) \\ 0 & 21.5 \\ 10 & 31.5 \\ 14 & 36.6 \\ 15 & 38 \\ 16 & 39.5 \\ 17 & 41 \\ 18 & 42.6 \\ 19 & 44.3 \\ 20 & 46 \end{array}$

Step 1

Prove that the given table satisfies the two properties needed for a probability distribution.

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Step 1.1

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 1.2

$21.5$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$21.5$ is not less than or equal to $1$

Step 1.3

$31.5$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$31.5$ is not less than or equal to $1$

Step 1.4

$36.6$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$36.6$ is not less than or equal to $1$

Step 1.5

$38$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$38$ is not less than or equal to $1$

Step 1.6

$39.5$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$39.5$ is not less than or equal to $1$

Step 1.7

$41$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$41$ is not less than or equal to $1$

Step 1.8

$42.6$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$42.6$ is not less than or equal to $1$

Step 1.9

$44.3$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$44.3$ is not less than or equal to $1$

Step 1.10

$46$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$46$ is not less than or equal to $1$

Step 1.11

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

Step 2

The table does not satisfy the two properties of a probability distribution, which means that the expectation mean can't be found using the given table.

Can't find the expectation mean