# mgf

• October 31st 2010, 10:13 PM
chutiya
mgf
for any constants y and z, the mgf of a random variable yX+z is given by

$M = e^{zt}M_{X}(yt)$

how do i prove this? can anyone give a hint?
• October 31st 2010, 10:17 PM
harish21
USE the defintion of moment generating function..

$M_{X}(t) = E(e^{tX})$

so,

$\displaystyle M_{yX+z}(t) = E[e^{(yX+z)t}]$

complete it........