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)
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)
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.