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1. The problem statement, all variables and given/known data

Given Z = X + Y.

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

2. Relevant equations

N.A.

3. 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?

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# Homework Help: Probability Mass Function of { Z | Z < 1 }, Z given Z is less than 1

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