Let $X_1,X_2,X_3$ be mutually stochastically independent random variables and let each of them have the following density function:
$f(x)= 2x$ when $0\leq x\leq 1$ and $f(x)=0$ elsewhere.
Let Y be the random variable defined as, $Y=\max(X_1, X_2, X_3)$, find (a) the distribution function and (b) the probability function of the random variable $Y$.
I saw somewhere that the distribution function of such variable to be given by $F_Y(y)=P(Y\leq y)=P(\max (X_1,X_2,X_3)\leq y)$.
If this is true, how may I apply it in this question to find (a) and (b) above?