Let $f ( x ) = 6 x ( 1 - x ) , 0

Name: Let $f ( x ) = 6 x ( 1 - x ) , 0 < x < 1$ be the probability density function of a random variable X. Find the mean of the probability density function $f$ . A) $\frac { 1 } { 3 }$ B) $\frac { 1 } { 6 }$ C) $\frac { 1 } { 2 }$ D)1 E)3 F)6 G)2 H)0
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Question

Let $f ( x ) = 6 x ( 1 - x ) , 0 < x < 1$ be the probability density function of a random variable X. Find the mean of the probability density function $f$ .
A) $\frac { 1 } { 3 }$ 
B) $\frac { 1 } { 6 }$ 
C) $\frac { 1 } { 2 }$ 
D)1
E)3
F)6
G)2
H)0

Quizplus · Accepted Answer

The mean of a probability density function $f(x)$ over the interval $[a, b]$ is given by $\int_a^b x f(x) \, dx$. For $f(x) = 6x(1-x)$ over $(0, 1)$, the mean is $\int_0^1 x \cdot 6x(1-x) \, dx = \frac{1}{2}$.

Let f(x)=6x(1−x),0<x<1f ( x ) = 6 x ( 1 - x ) , 0 < x < 1f(x)=6x(1−x),0<x<1

Let $f ( x ) = 6 x ( 1 - x ) , 0 < x < 1$