Working out the cumulative distribution

[millwallcrazy]

f(x) = 3(x^2)/(C^3) 0 < x < C
= 0 otherwise


Let the mean of the sample be Xa and let the largest item in the sample be Xm. What is the cumulative distribution for Xm?

 

[statdad]

I'm assuming that you are to work with a random sample of size $n$.

Note that for ANY continuous random variable, if $X_{max}$ is the maximum value, you know that $X_{max} \le a$ means that EVERY item in the sample is $\le a$, so that

$$G(a) = P(X_{max} \le a) = P(X_1 \le a \text{ and } X_2 \le a \text{ and } \dots \text{ and } X_n \le a)$$

Now, knowing that the $X$ values are independent (since they're from a random sample), what can you do with the statement on the right?