Hey there. I'm asked to prove:(adsbygoogle = window.adsbygoogle || []).push({});

If X1,...Xn are random variables defined on a set Ω and B1,...,Bn C R1 then prove that

(X1,...,Xn)^-1 (B1x...xBn) = X1^-1B1 n X2^-1B2 n ... n Xn^-1Bn

so I think I can explain the proof, but just not write it out. This is my attempt

if omega is on the left hand side:

the inverse image of X1^-1B1 is defined as all w in Ω such that X1(w) E B1 and that would apply to all Xi, Bi.

So the intersection of those events would be defined as all the w in Ω that

(X1,...,Xn)(w) E (B1x...xBn) which is the left hand side.

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# Proof of 2 sets being equal.

Can you offer guidance or do you also need help?

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