Expected value and variance of uniform distribution

Question

I have to find the expected value and variance of the uniform distribution X that is 0 for $x<1$ and $x>3$.

Also what is the probability $P(x>1.5)$?

Answer 1

Hint. The probability density function of the given continuous uniform distribution is

$$ f(x)=\begin{cases} \frac{1}{2} & \mathrm{for}\ 1 \le x \le 3, \\[8pt] 0 & \mathrm{for}\ x<1\ \mathrm{or}\ x>3, \end{cases} $$ giving $$ E(X)=\int_1^3x\cdot f(x)dx=\color{red}{?} $$ and $$ V(X)=\int_1^3x^2\cdot f(x)dx-\left(E(X) \right)^2=\color{red}{?} $$ One has $$ P(X>1.5)=\int_{1.5}^3f(x)dx=\color{red}{?} $$

Hope you can take it from here.