If the moment generating of X is M (t) = exp(100t + 200t^2), find:

1. the mean

2. the variance

3. P (160 < X < 180)

4. P (60 <= X <= 140)

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- Nov 2nd 2009, 10:53 AMaffelixIf the moment generating of X is M (t) = exp(100t + 200t^2)
If the moment generating of X is M (t) = exp(100t + 200t^2), find:

1. the mean

2. the variance

3. P (160 < X < 180)

4. P (60 <= X <= 140) - Nov 2nd 2009, 11:00 AMMoo
Hello,

E(X^n)=the n-th derivative of M(t) taken at t=0

And since the mean is E(X) and the variance is E(X²)-E(X)², you can do the first two questions easily.

The last two questions require that you recognize the distribution whose mgf is this one.