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**Probability Mass Function of { Z | Z < 1 }, "Z given Z is less than 1"**

## Homework Statement

Given Z = X + Y.

Find the probability density function of Z|Z < 1.

## Homework Equations

N.A.

## The Attempt at a Solution

f(z) = P(Z=z|Z<1) = P(Z=z AND Z < 1) / P(Z < 1).

I thought the top could be simplified to P(Z=z) for z < 1. Correct?

So,

f(z) = 0, for z > or = 1

f(z) = P(Z=z)/P(Z<1), for z < 1.

Correct?