Question

关于概率的问题.请各位指教,a) Let W and Z be independent random variables

Answer 1

a) I did this question before...It's just hard to write it out in text (I wish we have Latex here). I'll try my best...

The key to this questions is using CDF for derive PDF. I denote CDF as F(i.e. F_W() is CDF for W etc...) and PDF as f.

Since W, Z is uniformly over [-1,1], we know that F_W(t) = F_Z(t) = (t+1)/2.

Now let's consider X=W+Z. easy to know that X is over [-2,2]

F_X(t) = Prob(X