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I am given a moment-generation function $M_x(t)= e^{t+t^2}$ and asked to find the probability that the random variable is greater than $2.5$

Any help would be greatly appreciated!

user87683
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    Look up the moment generating function of the general normal (it was probably done in class and/or book. See what this means about $\mu$ and $\sigma^2$ in your example. – André Nicolas Jul 25 '13 at 15:00

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This is the mgf of a normal distribution. Note that $$M_{X}(t) = \exp \left(\mu t + \frac{\sigma^{2}t^{2}}{2} \right)$$

So $\mu = 1$ and $\sigma^{2} = 2$.

NebulousReveal
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