# probability question

• Nov 20th 2010, 07:10 AM
situation
probability question
just a quick question!

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

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

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

thanks :)
• Nov 20th 2010, 09:30 AM
CaptainBlack
Quote:

Originally Posted by situation
just a quick question!

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

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

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

thanks :)

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

CB