Is Y Gamma-Distributed If Y = 1 + X Where X ~ Gamma(k, θ)?

[ayazkhan]

I have a random variable X which is gamma-distributed with scale θ and shape k, i-e
X ~ gamma(k,θ);
Now I have another variable, Y= 1+X, is Y gamma-ditributed? if yes what will be the scale and shape parametrs for Y, and what will be the expression for the probability density function of Y.

Please help
Thanks in advance
Ayaz

 

[purplebird]

y = 1+x

p(y<Y) = cdf of y

p(1+X<Y)

P(X<Y-1) subst Y-1 in the cumulative density function of X and differentiate to get the pdf of X.