作业帮关于概率的问题.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-Zb) Let X and Y be independent random variables both with density:f(x)=3x^2 (if 0
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 02:53:16
![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-Zb) Let X and Y be independent random variables both with density:f(x)=3x^2 (if 0](/uploads/image/z/11515757-5-7.jpg?t=%E5%85%B3%E4%BA%8E%E6%A6%82%E7%8E%87%E7%9A%84%E9%97%AE%E9%A2%98.%E8%AF%B7%E5%90%84%E4%BD%8D%E6%8C%87%E6%95%99%2Ca%29+Let+W+and+Z+be+independent+random+variables+both+uniformly+distributed+on+%5B-1%2C1%5D.Derive+the+density+functions+of+W%2BZ+and+W-Zb%29+Let+X+and+Y+be+independent+random+variables+both+with+density%3Af%28x%29%3D3x%5E2+%28if+0)
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-Zb) Let X and Y be independent random variables both with density:f(x)=3x^2 (if 0
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
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-Zb) 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