fx(x) = 2x/x^2 is a pdf of random variable X
0 < x < c
Then
Fx(x) = x^2/c^2
Find moment generating function of Y
Y = 2x+10, note it is increasing.
X = (Y-10)/2 lets call this function g(y)
Fy(y)= Fx(g(y)) = 1/(c^2)*((y-10)/2))^2
No?
And when Fy(y) is found, it gives fy(y) = (y/c^2)*(1/2-1)
Then My(t) = E[e^(ty)] = 1/(c^2) * int[e^(ty)*y(1/2-1)dy] where we integrate from (10) to (2c+10)
Where I end up with
(1/tc^2)[(e^2ct+10)*(2c+10)-e^(2ct+10t)-(10e^10t-e^10t)]
But it this the mgf of Y?
My(t) = E(e^(ty)) = E(e^t(2x+10)) =e^(10t)*E{e^((2t)x)}
So, My(t) = e^(10t)*Mx(2t) This can be found by simple arithmetic calculation of mgf’s.