Question

Effect of scaling and offset on average and standard deviation. Suppose x is an n-vector
and α and β are scalars.
(a) Show that avg(αx + β1) = α avg(x) + β.
(b) Show that std(αx + β1) = |α| std(x).

Answer 1

Answer:

Explanation:

3.16 Effect of scaling and offset on average and standard deviation. Supposer is an n-vector and a and 8 are scalars. (a) Show that avg(ax +81) = o avg(s) + 8. (b) Show that star +81) = lastd(x). 3.17 Average and standard deviation of linear combination. Let 21,..., be n-vectors, and 01,..., be numbers, and consider the linear combination z = 12 + ... + (a) Show that avg(x) = 0; avg(x) + ... + avg(x). (b) Now suppose the vectors are uncorrelated, which means that for it), , and 1 are uncorrelated. Show that std(x) = a; std (x) +...+osto (1x).