cap_5_mont_p_09

SOLUCION INCORRECTA. LA SOLUCION CORRECTA INVOLUCRA TOMAR LIMITES. EJEMPLO

math P[X < a] = \lim_{t\to a} \int_{-\infty}^t f_X(x) dx = \lim_{t\to a} F_X(t) math mientras que: math P[X \leq a] = \int_{-\infty}^a f_X(x) dx = F_X(a) math

FAVOR CORREGIR

PUNTOS 0.0

=CAPITULO 5. EJERCICIO 09=

Si X es una variable aleatoria continua, demuestre que:

math P\left ( X1\leq X\leq X2 \right ) = P\left ( X1< X\leq X2 \right ) = P\left ( X1\leq X< X2 \right ) = P\left ( X1< X< X2 \right ) math

SOLUCIÓN: math P\left ( X1\leq X\leq X2 \right ) = P\left ( X1< X\leq X2 \right ) = P\left ( X1\leq X< X2 \right ) = P\left ( X1< X< X2 \right ) math

math \int_{X1}^{X2}f\left ( X \right )dX = \int_{X1}^{X2}f\left ( X \right )dX = \int_{X1}^{X2}f\left ( X \right )dX = \int_{X1}^{X2}f\left ( X \right )dX

math

math \left.X\right|_{X1}^{X2} = \left.X\right|_{X1}^{X2} = \left.X\right|_{X1}^{X2} = \left.X\right|_{X1}^{X2} math

math \left ( X2-X1 \right ) = \left ( X2-X1 \right ) = \left ( X2-X1 \right ) = \left ( X2-X1 \right) math

Solucionado por:
 * Juan Manuel López
 * Julian Cadena Isaza