Given: The given function is
[tex]f(x,y)=c(x-y)[/tex]
To find: Here we need to find the value of c for which f(x,y) will be a joint
discrete probability density function.
Solution:
Now, to find c we have,
[tex]\int\limits^3_{-2} \,\int\limits^2_0 {f(x,y)} \, dx dy\\=\int\limits^3_{-2} \,\int\limits^2_0 {c(x-y)} \, dx dy\\\\=\int\limits^3_{-2} \,[2c-2cy]dy\\=10c-5c\\=5c\\The integral should be1.\\So, 5c=1\\[/tex]
∴[tex]c=\frac{1}{5}[/tex]
Therefore, the required value of c is 1/5.
