Question

for the density function f(x) =2x÷9, 0<x<3the mean is​

Answer 1

Given : density function f(x) =2x/9,0<x<3,

To Find : mean

Solution:

f(x)   = 2x/9

integrating

$\int\limits^3_0 { \dfrac{2x}{9} } \, dx$

$= \dfrac{x^2}{9} \bigg |_0^3$

= 3²/9

= 1

Function verified   ( as total probability is 1 )

Mean   =∑xP(x)

hence integrating  x * 2x/9   = 2x²/9 over 0 to 3

Mean =

$\int\limits^3_0 { \dfrac{2x^2}{9} } \, dx$

$= \dfrac{2x^3}{27} \bigg |_0^3$

=  2(3)²/27  - 0

= 2

mean is​   2

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