Question

X is a uniformly distributed random variable that takes values between 0 and 1. The value of $E\left(X^3\right)$ will be

• A. 0
• B. 1/8
• C. 1/4
• D. 1/2

Answer 1

The correct option is C 1/4

Given that X is a uniformly distributed random variable that takes values between 0 and 1

$f\left(x\right)=(\begin{array}{cc}1;& 0\le x\le 1\\ 0;& x>1\end{array}$
$E\left\{x^3\right\}={\int }_0^{\infty }{x}^{3}f\left(x\right)\mathrm{dx}$

$={\int }_0^1{x}^3\mathrm{dx}=\frac{1}{4}{\left(x^4\right]}_0^1=\frac{1}{4}$