Replacing NaN with random variables that keep the standard deviation in MATLAB

I have a matrix A as a row vector containing some missing values NaN. Let's assume it looks like the following:

A = [2; NaN; 0.3; NaN; -0.8; NaN; 1; -0.5; NaN; 0.2];

The series has a A_mean = nanmean(A, 1) of 0.37 and a A_std = nanstd(A, 1) of 0.93.

I created a random vector B of the same size in

B = rand(1, 10)';

I defined an upper bound ub and a lower bound lb as

ub = A_mean * 5;
lb = A_mean * (-5);

So I changed B to

B = ub + (lb-ub) * rand(1, 10);

I can replace all NaN values in A by

idx = isnan(A);
A(idx) = B(idx);

Taking A_std = nanstd(A, 1) of this new defined vector leads to std, which is randomly different to 0.93.

I would like to know, whether I can replace the missing values NaN in A with random variables and keep the std the same?