作业帮关于概率的问题.请各位指教,
来源：学生作业帮 编辑：作业帮 分类：英语作业 时间：2024/05/13 13:31:05
关于概率的问题.请各位指教,
a) Let W and Z be independent random variables both uniformly distributed on [-1,1].Derive the density functions of W+Z and W-Z
b) Let X and Y be independent random variables both with density:
f(x)=3x^2 (if 0
a) Let W and Z be independent random variables both uniformly distributed on [-1,1].Derive the density functions of W+Z and W-Z
b) Let X and Y be independent random variables both with density:
f(x)=3x^2 (if 0
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
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