1. Fix a positive integer n. Recall that R" is equipped with the standard inner-product (v, w) = ER UkWk for v, w E R", and it induces the standard Euclidean norm lull = (v, v)i. The standard normal density in R" is =: (1)SHE ud 1 Lull2 (27) 2 (1) which for n = 1 and n = 2 look, respectively, like and (a) i. (1 point) Fix n = 1, sample 10* points independently from the standard normal distribution in R", and plot a histogram, with bin width 10-1, of the absolute values of the sampled points. ii. (1 point) Fix n = 10, sample 10* points independently from the standard normal distribution in R", and plot a histogram, with bin width 10", of the norms of the sampled points. iii. (1 point) Fix n = 103, sample 10* points independently from the standard normal distribution in R", and plot a histogram, with bin width 10-1, of the norms of the sampled points