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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

I'm looking at the following random variables:

$Z_1$ is normally distributed with zero mean and variance $\sigma _1 ^2$

$Z_2$ is normally distributed with zero mean and variance $\sigma _2 ^2$

$B$ is Bernoulli with probability of success $p$.

$X$ is a random variable that takes $Z_1$ if $B=1$ and $Z_2$ if $B=0$.

What is the variance of $X$?