Matemática discreta Ejemplos

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

Paso 1

Una variable aleatoria discreta $x$ toma un conjunto de valores separados (como $0$ , $1$ , $2$ ...). Su distribución de probabilidad asigna una probabilidad $P (x)$ a cada valor posible $x$ . Para cada $x$ , la probabilidad $P (x)$ cae entre $0$ y $1$ inclusive y la suma de las probabilidades para todos los posibles valores de $x$ es igual a $1$ .

1. Para cada $x$ , $0 \leq P (x) \leq 1$ .

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

Paso 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 $0$

Paso 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 $0$

Paso 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 $0$

Paso 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 $0$

Paso 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 $0$

Paso 7

La probabilidad $P (x)$ no cae entre $0$ y $1$ inclusive para todos los valores $x$ , lo que no cumple con la primera propiedad de la distribución de probabilidad.

La tabla no cumple con las dos propiedades de una distribución de probabilidad.