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Probability Mass Function of { Z | Z < 1 }, "Z given Z is less than 1"
Given Z = X + Y.
Find the probability density function of Z|Z < 1.
N.A.
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?
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?