An investor invests 100 dollars in a stock. The return X (in dollars) after 10 years...

Question:

An investor invests 100 dollars in a stock. The return X (in dollars) after 10 years has
MGF given by M(t) = exp(180t + 800(t^2)).
(a) Find the mean, variance and standard deviation of the return.
(b) Find the probability that the return is more than the initial investment.
(c) Find the probability that the return is in between 150 and 200 dollars.
(d) If Y = e^(X−100), find the density of Y .

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