A quiz flashcard has the following:
X(sub 1), X(sub 2), ... , X(sub n) are IID random variables. State the CDF of the first order statistic, X(sub 1).
Fx(sub 1)(x)= 1 - [1-Fx(x)]^n
Equivalently
Sx(sub 1)(x) = [Sx(x)]^n
Since the survival function is 1- F(x), why does the first solution have 1 minus the [1-Fx(x)]^n?
Also, the survival function is typically denoted as S(x). Is there such a function that is s(x), or akin to the pdf/cdf relation [f(x)/F(x)]? If so, what are the applications? Or is s(x) simply the derivative of S(x)?
X(sub 1), X(sub 2), ... , X(sub n) are IID random variables. State the CDF of the first order statistic, X(sub 1).
Fx(sub 1)(x)= 1 - [1-Fx(x)]^n
Equivalently
Sx(sub 1)(x) = [Sx(x)]^n
Since the survival function is 1- F(x), why does the first solution have 1 minus the [1-Fx(x)]^n?
Also, the survival function is typically denoted as S(x). Is there such a function that is s(x), or akin to the pdf/cdf relation [f(x)/F(x)]? If so, what are the applications? Or is s(x) simply the derivative of S(x)?
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