Answer the following questions a$,$ b$,$ c$,$ d with true or false

Let $x_1,$dots,$x_5$ be defined on $(,F,P)$ and be i$.$i$.$d$.$ with distribution $P$ on $R$ given by the density

$f(x)=\frac{1}{2}{1}_{[-1,1]}(x),$xinR.

Determine whether each of the following statements is true or false.

a$.$ The mean of $x_1$ is $0.$

b$.$ The variance of $x_1$ is $\frac{1}{2}.$

c$.$ The median of $P$ is $0.$

d$.$ All moments of $P$ of odd order are zero.