for any constants y and z, the mgf of a random variable yX+z is given by

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

how do i prove this? can anyone give a hint?

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- Oct 31st 2010, 10:13 PMchutiyamgf
for any constants y and z, the mgf of a random variable yX+z is given by

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

how do i prove this? can anyone give a hint? - Oct 31st 2010, 10:17 PMharish21
USE the defintion of moment generating function..

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

so,

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

complete it........