I have a set of distributions and I have combined (programmatically, not mathematically) them with weights, for example: Dist1, Dist2, Dist3, Dist4 p=.25, p=.20, p=.20, p=.35
Unless I am mistaken, the overall mean of this combination can be determined as:
mean(dist1) * 0.25 + mean(dist2) * .20 + mean(dist3) * .20 + mean(dist4) * .35
the probability of any value (e.g. pdf(x)) is calculated in much the same way:
pdf(x, Dist1) * .25 + pdf(x, Dist2) * .20 + pdf(x, Dist3) * .20 + pdf(x, Dist4) * .35
But the standard deviation cannot be determined like that. Other answers I have found on this site are for working with samples of finite length, but here I already know the standard deviations of my distributions and want to somehow combine them. I also saw somewhere that I can combine standard deviations by doing sqrt(std1^2 + std2^2) but I don't know how the weighting would come into this.
How can I do this? (and does what I have already done work mathematically - it almost seems too simple to be correct).
