Finding Derivative, Moment Generating Function

**Relmiw** · October 23rd 2011, 01:34 PM

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))

**Auri** · October 23rd 2011, 02:58 PM

Are you trying to see if the second derivative is correct?

**Relmiw** · October 23rd 2011, 02:59 PM

Yes, that's exactly it.

**Auri** · October 23rd 2011, 03:19 PM

First factor out the constant, then use the chain rule.
$0.01Y(d/dt(e^(.01tY)) + 50(d/dt(e^(50t))$
$0.01Y(e^(.01tY)(d/dt(.01tY)) + 50e^(50t)(d/dt(50t))$
$0.0001Ye^(0.01tY)(d/dt(tY)) + 2500e^(50t)$
$0.0001Y^2e^(0.01tY)+2500.e^(50t)$
Scheiße I can't use the formatting text correctly.

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