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Let $p(x | \mu, \sigma)$ be a unimodal symmetric probability density function with mean $\mu$ and variance $\sigma^2$. For generality, let's assume $p$ is non-Gaussian p.d.f.

Now I have a sequence of $p_i(x) = p(x | \mu_i, \sigma_i)$. Then I consider their joint p.d.f. $\Pi(x) \sim \prod_{i=1}^N p_i(x)$. When $\Pi(x)$ is also unimodal? Maybe there are some results on this?

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