I think I'm doing this wrong, but I can't see where. Y is a random variable.
m'(t) = Expected Value (50 * e^(t*50) + 0.01 * Y * e^(t*0.01*Y))
m''(t) = Expected Value (50^2 * e^(t*50) + (0.01 * Y)^2 * e^(t*0.01*Y))
I think I'm doing this wrong, but I can't see where. Y is a random variable.
m'(t) = Expected Value (50 * e^(t*50) + 0.01 * Y * e^(t*0.01*Y))
m''(t) = Expected Value (50^2 * e^(t*50) + (0.01 * Y)^2 * e^(t*0.01*Y))
First factor out the constant, then use the chain rule.
$\displaystyle 0.01Y(d/dt(e^(.01tY)) + 50(d/dt(e^(50t))$
$\displaystyle 0.01Y(e^(.01tY)(d/dt(.01tY)) + 50e^(50t)(d/dt(50t)) $
$\displaystyle 0.0001Ye^(0.01tY)(d/dt(tY)) + 2500e^(50t)$
$\displaystyle 0.0001Y^2e^(0.01tY)+2500.e^(50t)$
Scheiße I can't use the formatting text correctly.