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## Main Question or Discussion Point

forgive for my ignorance, but i have a practical problem that i dont know how to approach:

[tex]X\sim\mathcal{N}(\mu,\sigma^2)[/tex]

where [tex]\mu\sim\mathcal{N}(\mu_{\mu},\sigma_{\mu}^2)[/tex]

and [tex]\sigma\sim\mathcal{N}(\mu_{\sigma},\sigma_{\sigma}^2)[/tex]

what is the resulting distribution of [tex]X[/tex], in terms of [tex]\mu_{\mu},\sigma_{\mu},\mu_{\sigma},\sigma_{\sigma}[/tex]?

[tex]X\sim\mathcal{N}(\mu,\sigma^2)[/tex]

where [tex]\mu\sim\mathcal{N}(\mu_{\mu},\sigma_{\mu}^2)[/tex]

and [tex]\sigma\sim\mathcal{N}(\mu_{\sigma},\sigma_{\sigma}^2)[/tex]

what is the resulting distribution of [tex]X[/tex], in terms of [tex]\mu_{\mu},\sigma_{\mu},\mu_{\sigma},\sigma_{\sigma}[/tex]?