Is there a known result about what is the distribution of the sum of constant and a exponentially distributed random variable?
If so, can someone refer me to an article or an e book with this information?
Do you mean Y = a + X, where X is exponentially distributed and a is a constant?
If so P(Y < y) = P(a + X < y) = P(X < y - a).
yes, this is what I meant.
But I need to know if Y has any known distribution. I am interested in the expectation of Y
maybe it remains exponentially distributed but with different parameter (y=a+X)? and if so where I can find the proof...