Question

A hypercube with side length 1 in d dimensions is defined to be the set of points (x1, x2, ..., xd) such that 0≤xj≤1 for all j = 1, 2, ...,
d. the boundary of the hypercube is defined to be the set of all points such that there exists a j for which 0≤xj≤.05 or .95≤xj≤1 (namely, the boundary is the set of all points that have at least one dimension in the most extreme 10% of possible values). what proportion of the points in a hypercube of dimension 50 are in the boundary? (hint: you may want to calculate the volume of the non-boundary region) please give your answer as a value between 0 and 1 with 3 significant digits. if you think the answer is 50.52%, you should say 0.505:

Answer 1

Answer:

Step-by-step explanation:

We know that the volume of the whole hypercube is 1^50 = 1.

The volume of the interior of the hypercube is 0.9^50 = 0.005.

Thus, the volume of the boundary is 1-0.005 = 0.995.