Marginal density functions: $f_{V}(v)=f_{W}(w)=\frac{1}{60}$
Joint density function: $f_{V,W}(v,w)=\frac{1}{3600}$, for $0\leq x\leq60$ and $0\leq y\leq60$
I need to find the cumulative density function of $T = W - V$
I'm thinking it's something along the lines of this:
$F_{t}(t)=\left\{\begin{matrix} 0 & w-v<0\\ \frac{t}{60} & 0 \leq w-v \leq 60\\ 1 & w-v>60 \end{matrix}\right.$
Any help appreciated.
Thanks!
There are two ways of getting the density function…
1.) by convolution formuar
$V,W$ are independent RV (why?) so are $W$ and $-V$ and so the density of $T = W + (-V)$ is the convolution of the densities of $W$ and $-V$ which are known…
2.) $$f_T(t) = F'_T(t) = \int_{W-V \le t} f_{(V,W)}(v,w)\; dv dw$$ what can be calculated easily…