Cumulative element-wise average from 3D matrix

My dataset is a 3D matrix (3x5x2). How can I create a new 3x5x2 matrix where the respective elements in the 1st dimension are cumulatively averaged across the 2nd dimension?

I want a new matrix that in which:

(:,1,1) and (:,1,2) remain the same (the average of each 1st element in first dimension is itself).

(:,2,1) and (:,2,2) are the average of the first 2 elements in each respective row (i.e. 2nd dimension).

(:,3,1) and (:,3,2) are the average of the first 3 elements in each respective row, and so on....

For example,

A = rand(3,5,2)

A(:,:,1) =

0.3444 0.9392 0.7279 0.2141 0.7071

0.8340 0.0112 0.3847 0.1898 0.9043

0.6843 0.4466 0.8988 0.2104 0.2948

A(:,:,2) =

0.5756 0.6006 0.4804 0.6754 0.1328

0.5651 0.8882 0.3092 0.5088 0.7747

0.8765 0.9748 0.6653 0.0476 0.1058

With the above A, I want to creat the below (new) matrix of cumulatively averaged respective rows.

A_new(:,:,1) =

0.3444 0.6418 0.6705 0.5564 0.5865

0.8340 0.4226 0.4100 0.3549 0.4648

0.6843 0.5655 0.6766 0.5600 0.5070

A_new(:,:,2) =

0.5756 0.5881 0.5522 0.5830 0.4930

0.5651 0.7267 0.5875 0.5678 0.6092

0.8765 0.9257 0.8389 0.6411 0.5340

Answer 1

[Walter Roberson]

A_new = cumsum(A, 2) ./ (1:size(A,2));

[J Toole]

Perfect, thank you very much.