If the economy booms, RTF$,$ Inc. stock is expected to return $10$ percent. If the economy goes into a recessionary period, then RTF is expected to only return $5$ percent. The probability of a boom is $62$ percent while the probability of a recession is $38$ percent. What is the variance of the returns on RTF$,$ Inc. stock?

Multiple Choice

$0\mathrm{.}000810$

$0\mathrm{.}001881$

$0\mathrm{.}024037$

$0\mathrm{.}000589$

$0\mathrm{.}000190$