Cap_5_mont_p_23

OK PUNTOS 0.7

=CAPITULO 5, PROBLEMA 23=

Suponga que: math f\left ( x \right ) = 2.0 math Determinar la media y la varianza de x para 49.75<x<50.25

SOLUCION

MEDIA math \mu = E_{X}\left [ x \right ]=\int_{-\infty }^{\infty }xf\left ( x \right )dx math

math \mu =\int_{49.75}^{50.25}x*2.0dx math

math \mu =\left. {x^{2}} \right|_{49.75}^{50.25} math

math \mu ={49.75^{2}}-{50.25^{2}} math

math \mu =50 math

VARIANZA math \sigma ^{2} =\int_{-\infty }^{\infty }x^{2}f\left ( x \right )dx - \mu math

math \sigma ^{2} =\int_{49.75}^{50.25}x^{2}*2.0dx - \mu^{2} math

math \sigma ^{2} =2*\left. \frac{x^{3}}{3} \right|_{49.75}^{50.25} - \mu^{2} math

math \sigma ^{2} =\left (2*\frac{50.25^{3}}{3}-2*\frac{\left 49.75^{3} \right }{3} \right ) - 50^{2} math

math \sigma ^{2}= 0.0208 math

Solucionado por:
 * Alexandra Reyes G.
 * David Camilo Osorio A.
 * Diana Ramirez.