cap_5_mont_p_20

=OK PUNTOS 0.7=

=CAPITULO 5,EJERCICIO 20=

Suponga que f(x)= 0,25 para 0 < x < 4. Determine la media y la varianza de X.

MEDIA math \mu =E\left [ X \right ]=\int_{-\infty }^{\infty }x f_X(x)dx math math \mu =E\left [ X \right ]=\int_{0 }^{4 }x f_X(x)dx math math \mu =E\left [ X \right ]=\int_{0 }^{4 }x (0,25)dx math math \mu =E\left [ X \right ]=\left. \frac{0,25*x^{2}}{2} \right|_0^4 math math \mu =E\left [ X \right ]=\left [\frac{0,25*(4)^{2}}{2} \right ]-\left [\frac{0,25*(0)^{2}}{2} \right ] math math \mu =E\left [ X \right ]=2 math

VARIANZA math \sigma ^{2}=V\left [ X \right ]=\int_{-\infty }^{\infty }(x-\mu)^{2}f(x)dx=\int_{-\infty }^{\infty }x^{2}f(x)dx-\mu^{2} math math \sigma ^{2}=V\left [ X \right ]=\int_{0}^{4}x^{2}(0,25)dx-(2)^{2} math math \sigma ^{2}=V\left [ X \right ]=\left. \frac{0,25*x^{3}}{3} \right|_0^4 -(2)^{2} math math \sigma ^{2}=V\left [ X \right ]= \left [\left (\frac{0,25*(4)^{3}}{3} \right ) -\left (\frac{0,25*(0)^{3}}{3} \right ) \right ] -(2)^{2} math math \sigma ^{2}=V\left [ X \right ]= 1,33 math

RESUELTO POR:
 * BRENDA PEÑA
 * FELIPE TRUJILLO