(Solved): Can anyone solve this whole problem? Using R studio. (a) Write a function with input n and d and ou ...

(a) Write a function with input $n$ and $d$ and output $n$ IID random vector uniformly distributed within $d$-dimensional unit ball (with radius 1 ). (b) For two random vectors in 3D unit ball, what is the expected distance between them? Do not calculate it theoretically. Do a simulation to estimate the expected distance. (c) Let ${?}_d$ be the ratio between the volume of a unit ball and the volume of a cube with side 2 , in ${\mathbb{R}}^d$. Estimate ${?}_d$ for $d=2,\dots ,5$. (d) Search online and find the exact values of ${?}_d$. Compare it with your estimate.