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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?

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    You are on the right track. $\mathbb{P}(Y \leq y) = \mathbb{P}(\max(X_1,X_2,X_3) \leq y)$. Note that $\max(X_1,X_2,X_3) \leq y$ is equivalent to $X_1 \leq y$ and $X_2 \leq y$ and $X_3 \leq y$ and make use of the fact that $X_1,X_2,X_3$ are independent.2011-12-22

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