Variance of a two-regime return

MediumRandom Variables Statistics~4m

A trading day is "calm" with probability $0.7$ and "volatile" with probability $0.3$ . On a calm day the return is Normal with mean $0$ and standard deviation $1\%$ ; on a volatile day it is Normal with mean $0$ and standard deviation $3\%$ . What is the variance of a single day's return (in $\%^2$ )? Give a decimal to two places.

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Condition on the regime - law of total variance.
The means match, so only the average within-regime variance survives.

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3.4 (± 0.01)

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Variance of a two-regime return

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