Statistics Examples

$\begin{array}{c} x & P (x) \\ 0 & 0.23 \\ 1 & 0.37 \\ 2 & 0.22 \\ 3 & 0.13 \\ 4 & 0.03 \\ 5 & 2.01 \\ 6 & 0.01 \end{array}$

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

$0.23$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.23$ is between $0$ and $1$ inclusive

Step 3

$0.37$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.37$ is between $0$ and $1$ inclusive

Step 4

$0.22$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.22$ is between $0$ and $1$ inclusive

Step 5

$0.13$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.13$ is between $0$ and $1$ inclusive

Step 6

$0.03$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.03$ is between $0$ and $1$ inclusive

Step 7

$2.01$ is not less than or equal to $1$ , which doesn't meet the first property of the probability distribution.

$2.01$ is not less than or equal to $1$

Step 8

$0.01$ is between $0$ and $1$ inclusive, which meets the first property of the probability distribution.

$0.01$ is between $0$ and $1$ inclusive

Step 9

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