P(M > 0.7 (intersection) (X1,...,XN) <= 0.8)/ (0.8^N)
I think I have a proposed way to get the intersection.
Since the maximum will be greater 0.7 and we know all the variables have an upper limit of 0.8.
The cumulative distribution function of the maximum will be evaluated with the limits of integration being 0.7 for the lower bound and 0.8 for the upper bound.
The pdf of the maximum of N independent uniform random variables is given by
f(x) = n * (x^(n-1))
So the integral from 0.7 to 0.8 will give us .
And taking the denominator I mentioned above getting a final answer of
Does this line of reasoning suit everyone?