The problem and its solution is posted below. The question that I need to ask will follow:
Problem:
Solution:
My Question:
If one analyzes the multiple choice answers, one arrives at a very nice antiderivative when evaluating the Probability Density Function contained in the Expected Value for E. Indeed, this turns out to be the answer. I am not asking how to solve this problem via the process of elimination, though.
My question is as follows:
How, when evaluating max(X1, X2, X3, X4), is it possible to conclude that Fmax(x) = F(x)^4?
I understand that these events are independent and that each share a Continuous Probability Density Function. I also understand that Independent Probability Density Functions, when applied to a sequence of events, can lead to them being multiplied, but I do not recall any of this happening with the Cumulative Distribution Function, let alone what this has to do with finding the maximum of the four bids. Please help. Thanks for your guys' time.
Problem:
Solution:
My Question:
If one analyzes the multiple choice answers, one arrives at a very nice antiderivative when evaluating the Probability Density Function contained in the Expected Value for E. Indeed, this turns out to be the answer. I am not asking how to solve this problem via the process of elimination, though.
My question is as follows:
How, when evaluating max(X1, X2, X3, X4), is it possible to conclude that Fmax(x) = F(x)^4?
I understand that these events are independent and that each share a Continuous Probability Density Function. I also understand that Independent Probability Density Functions, when applied to a sequence of events, can lead to them being multiplied, but I do not recall any of this happening with the Cumulative Distribution Function, let alone what this has to do with finding the maximum of the four bids. Please help. Thanks for your guys' time.
