- #1

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- 0

= 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?

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- Thread starter millwallcrazy
- Start date

- #1

- 14

- 0

= 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

statdad

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

[tex]

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)

[/tex]

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

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