probability question

just a quick question!

For $\displaystyle n \geq 1$, let $\displaystyle X_1,X_2,....,X_n$ denote $\displaystyle n$ independent and identically distributed random variables according to $\displaystyle X$, with cdf $\displaystyle F_X(y)$. Let $\displaystyle Y = max\{X_1,X_2,....,X_n \}$. Show that the cdf $\displaystyle F_Y(y)$ of $\displaystyle Y$ satisfies:

$\displaystyle F_Y(y)=(F_X(y))^n \ y\in \Re$

that is meant to be y in the real numbers but cant find what the latex is for it.

thanks :)

Quote:

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Originally Posted by situation

just a quick question!

For $\displaystyle n \geq 1$, let $\displaystyle X_1,X_2,....,X_n$ denote $\displaystyle n$ independent and identically distributed random variables according to $\displaystyle X$, with cdf $\displaystyle F_X(y)$. Let $\displaystyle Y = max\{X_1,X_2,....,X_n \}$. Show that the cdf $\displaystyle F_Y(y)$ of $\displaystyle Y$ satisfies:

$\displaystyle F_Y(y)=(F_X(y))^n \ y\in \Re$

that is meant to be y in the real numbers but cant find what the latex is for it.

thanks :)

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$\displaystyle P(Y\le y)=P((X_1\le y)\wedge (X_2\le y) \wedge ... \wedge (X_n\le y))=P(X_1\le y) P(X_2\le y) ... P(X_n\le y))$

CB