suppose $X$ is a random variable with Bernoulli distribution and $P=0/5$ and $Y $ is Random variable independent of the $X$ with Distribution function $F$. how can I calculate Distribution function $Z=X+Y$
2026-04-02 15:58:06.1775145486
calculating Distribution function $Z=X+Y$
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You could start with:
$$F_Z(x)=\Pr(X+Y\leq x)=$$$$\Pr(1+Y\leq x\wedge X=1)+\Pr(Y\leq x\wedge X=0)$$ And applying independence.