# #StackBounty: #sampling #multivariate-analysis #multivariate-normal how to construct and sample from conditional multi-variate normal d…

### 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?

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