*Bounty: 50*

*Bounty: 50*

The two random variables D and W representing the uncertainty around the daily and weekly prices. Both random variables follow a normal distribution. I want a probability distribution function (perhaps multi-variate and conditional) to represent the uncertainty around these two variables (Q1). Secondly, I want to get N samples, e.g. using the classic monte Carlo method (Q2).

For instance, let’s say $w_1, w_2, …, w_n$ represents the uncertainty around the weekly price with a mean of $overline{w}$ and a standard deviation of $sigma_w$. For each weekly sample, $w_i$, the daily price samples should have a mean equal to the corresponding weekly sample and the standard deviation as a function of the corresponding weekly price.

To better explain, $D_{wi}^{dj}, j=1:M$ are M daily price sample corresponding the weakly sample $w_i$. The mean of $D_{wi}^{dj}, j=1:M$ is equal to $w_i$ and its STD is $w_i / 10$.

How can I address Q1 and Q2 (finding the probability distribution function and sampling from it) for the given problem?