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I have 2 normally distributed random variable $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows:

$H_0 \sim N(\mu_0, \sigma_0)$

$H_1 \sim N(\mu_1, \sigma_1)$

$H = p * H_1 + (1-p) * H_0$

The mean value $\mu$ of the combined distribution $H$ is:

$\mu = p * \mu_1 + (1-p) * \mu_0$

Now, what is the standard deviation $\sigma$ of $H$?

Is there a simple formula for $\sigma$, in terms of $p, \mu_0, \sigma_0, \mu_1, \sigma_1$?

I have 2 normally distributed random variable $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows:

$H_0 \sim N(\mu_0, \sigma_0)$

$H_1 \sim N(\mu_1, \sigma_1)$

$$f_H = p * f_1(x) + (1-p) * f_0(x),$$

where $H$ has pdf $f_H$ and $H_1$ and $H_0$ have pdfs $f_1$ and $f_0$ respectively. The mean value $\mu$ of the combined distribution $H$ is:

$\mu = p * \mu_1 + (1-p) * \mu_0$

Now, what is the standard deviation $\sigma$ of $H$?

Is there a simple formula for $\sigma$, in terms of $p, \mu_0, \sigma_0, \mu_1, \sigma_1$?

I have 2 normal distributions $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows:

$H_0 = N(\mu_0, \sigma_0)$

$H_1 = N(\mu_1, \sigma_1)$

$H = p * H_1 + (1-p) * H_0$

The mean value $\mu$ of the combined distribution $H$ is:

$\mu = p * \mu_1 + (1-p) * \mu_0$

Now, what is the standard deviation $\sigma$ of $H$?

Is there a simpe formula for $\sigma$, in terms of $p, \mu_0, \sigma_0, \mu_1, \sigma_1$?

I have 2 normally distributed random variable $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows:

$H_0 \sim N(\mu_0, \sigma_0)$

$H_1 \sim N(\mu_1, \sigma_1)$

$H = p * H_1 + (1-p) * H_0$

The mean value $\mu$ of the combined distribution $H$ is:

$\mu = p * \mu_1 + (1-p) * \mu_0$

Now, what is the standard deviation $\sigma$ of $H$?

Is there a simple formula for $\sigma$, in terms of $p, \mu_0, \sigma_0, \mu_1, \sigma_1$?