8 views

1 vote

Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian distributed with mean $\mu_{2}$ and variance $\sigma_{2}^{2}$. Then the distribution of $X$ is

- Gaussian random variable with mean $\mu_{2}$ and variance $\sigma_{1}^{2}+\sigma_{2}^{2}$.
- Uniform with mean $\mu\left(\sigma_{1}^{2}+\sigma_{2}^{2}\right)$.
- Gaussian random variable with mean $\mu_{2}$ and variance $\sigma_{1}^{2}+\sigma_{2}^{2}$.
- Has no known form.
- None of the above.