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I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where

**c**is a constant in ℝ

I tried to calculate it in the following way:

[tex] \int^∞_0 e^{(z+c)t} f(z+c)dz[/tex] where [tex] f(z) [/tex] is an exponential pdf with parameter λ.

but it proved to be an unsuccessful method. Could anyone please show me the right direction? I know I could use Jacobian transformation but I'm sure there is an easier method.

Thank you in advance!