# Working out the cumulative distribution

1. May 8, 2010

### 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?

2. May 8, 2010

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?