I have $$X(t), -\infty \leq t \leq \infty $$ as a Poisson process with parameter $ \lambda $ and then $$Y(t) = X(t)-tX(1), 0 \leq t \leq 1$$
When I find the mean of $Y(t)$, I simply do $ E(Y(t)) = E(X(t)) - tE(X(1))$ which gives $\mu_Y = \lambda(1-t)$
But the textbook answer says $\mu_Y = 0$. I'm wondering what I'm missing out.