If the moment generating function of a random variable X is given by
Mx(t) = e(3t +8t^2), find the mean and variance of X.
2006-11-20 17:16:29 · 3 answers · asked by NONE N 1 in Science & Mathematics ➔ Mathematics
to find the mean and variance of a MGF you need to find the moments. To find the first moment, take the first derivative and then set t=0. This would be (3 + 16t)*e^(3t + 8t^2). With t=0 this equals 3. The second moment is equated from the second derivative. This is 16*e^(3t + 8t^2) + (e^(3t + 8t^2))*(3+16t)^2. With t=0 the second moment equals 16 + 9 = 25.
The mean is the first moment when t=0. This equals 3.
The variance is the second moment minus the first moment squared. This equals 25 - 9 = 16.
2006-11-23 01:56:13 · answer #1 · answered by Mike 2 · 0⤊ 0⤋
Is that Mx(t) = e^(3t +8t^2) ??
2006-11-21 12:54:16 · answer #2 · answered by Leltos 5 · 0⤊ 0⤋
tricky aspect. research in yahoo. that will might help!
2014-11-02 04:11:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋