Mathematica Mathematical Modelling Question

[Hummingbird25]

HELP: Mathematical Modelling Question

Hi

Given X_1 \ldots X_n be stochastic independent variables with the distribution functions F_X_{1}, \ldots ,F_X_{n}. U = min(X_1 \ldots X_n) and V = min(X_1 \ldots X_n).

F_{U} and F_{V} for U and V, and let F_{U,V} be simultaneously distribution functions for the stochastic vectors (U,V).

Then show that

F_{V} (s) = \Pi \limit_{i=1} ^{n} F_{X_i} (s) where \forall s \in \mathbb{R}

I can see that if I expand the sum I get

F_X_{1}(s) + F_X_{2}(s) + F_X_{3}(s) + \ldots + F_X_{i}(s) where 1 \leq i \leq n

Doesn't that mean that

F_X_{1}(s) + F_X_{2}(s) + F_X_{3}(s) + \ldots + F_X_{i}(s) = (F_X_{1}(s) \ \mathrm{U} \ F_X_{2}(s) \ \mathrm{U} F_X_{3}(s) \ \mathrm{U} \ \ldots \ \mathrm{U} \ F_X_{n}(s)) ??

Since \sum_{i=1} ^{n} P(A_i) = P(A_1) + P(A_2) + P(A_3) + \ldots + P(A_n)

Sincerely
Hummingbird

 

[HallsofIvy]

May we assume that
V = min(X_1 \ldots X_n)
was actually supposed to be
V = max(X_1 \ldots X_n)

 

[Hummingbird25]

My assignment uses U and V to distingues between min and max, but I guess it doesn't make that a bit a difference in the final calculation.

Sincerely Humingbird

May we assume that
V = min(X_1 \ldots X_n)
was actually supposed to be
V = max(X_1 \ldots X_n)