## Estimating parameters from multivariate normal

I need to estimate parameters from data that follow a mutinormal distribution. The parameters that I need to estimate are contained in the expression for the mean of the marginal normal distributions. That is each marginal distribution has mean:

$$\frac{p_1*c_i + p_1*y}{p_1+p_2}$$

where $$p_1$$, $$p_2$$ and $$y$$ are the paramters that I need to estimate and $$c_i$$ is just a known contant associated with the ith marginal. $$p_1$$ and $$p_2$$ are random parameters and $$y$$ is a fixed parameter.

I've tried using a multinormal likelihood approach, which gives an estimate for the mean as the sample mean, but how do I get estimate of the actual parameters from this sample mean? Can I even use this approach?

Also is there an added complexity to estimating parameters when there are random parameters, as is the case with $$p_1$$ and $$p_2$$?

Any help, on how best to estimate the paramters $$p_1$$, $$p_2$$ and $$y$$ would be great?

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