cap_4_mont_p_24

OK SIN EMBARGO HABIAN ERRORES EN FORMULAS QUE YA CORREGI. PUNTOS 0.7

Capítulo 4, Problema 24
Determinar la función de distribución acumulada de la variable aleatoria:


 * X || -2 || -1 || 0 || 1 || 2 ||
 * f(x) || 0.125 || 0.25 || 0.25 || 0.25 || 0.125 ||

Y determine las siguientes probabilidades: math P\left ( x\leq 1.25 \right ) math math P\left ( x\leq 2.2 \right ) math math P\left ( -1.1< x\leq 2.2 \right ) math math P\left ( x> 0 \right ) math

Solución:

Función de distribucion acumulada: math F_X(x)= P(X \leq x)= \sum_{x_{i}\leq x} p_x(x_i) math

De esta maneras tenemos que: math p\left ( x\leq -2 \right )= p\left ( X= -2 \right ) =\frac{1}{8} math math p\left ( x\leq -1 \right )= p\left ( X= -2 \right )+p\left ( X= -1 \right ) =\frac{1}{8}+\frac{2}{8}=\frac{3}{8} math math p\left ( x\leq 0 \right )= p\left ( X= -2 \right )+ p\left ( X= -1 \right )+ p\left ( X= 0 \right ) =\frac{1}{8}+\frac{2}{8}+\frac{2}{8}=\frac{5}{8} math math \\ p\left ( x\leq 1 \right ) = p\left ( X= -2 \right )+ p\left ( X= -1 \right )+ p\left ( X= 0 \right )+ p\left ( X= 1 \right ) =\\ =\frac{1}{8}+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}=\frac{7}{8} math math \\ p\left ( x\leq 2 \right )=p\left ( X= -2 \right )+ p\left ( X= -1 \right )+ p\left ( X= 0 \right )+ p\left ( X= 1 \right )+ p\left ( X= 2 \right )=\\ =\frac{1}{8}+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}+\frac{1}{8}=\frac{8}{8} math

Ahora, resolvamos las probabilidades:

math P\left ( x\leq 1.25 \right )= p\left ( X= -2 \right )+ p\left ( X= -1 \right )+ p\left ( X= 0 \right )+ p\left ( X= 1 \right ) =\frac{1}{8}+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}=\frac{7}{8} math math P\left ( x\leq 2.2 \right )=p\left ( X= -2 \right )+ p\left ( X= -1 \right )+ p\left ( X= 0 \right )+ p\left ( X= 1 \right )+ p\left ( X= 2 \right ) =\frac{1}{8}+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}+\frac{1}{8}=\frac{8}{8} math math P \left ( -1.1< x\leq 2.2 \right )= p\left ( X= 0 \right )+p\left ( X= 1 \right )+p\left ( X= -1 \right ) =\frac{2}{8}+\frac{2}{8}+\frac{2}{8}=\frac{6}{8} math math P\left ( x> 0 \right )= 1-p\left ( x\leq 0 \right ) = 1-\frac{5}{8}= \frac{3}{8} math

Solucionado por:
 * Grupo 11