Working out the cumulative distribution

[millwallcrazy]

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

<br /> 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)<br />

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?