Question

Determine the value of c that makes the function f(x y) = c/x-y/ a joint discrete probability density function for x=2,0,2 and y=-2,3

Answer 1

Given:  The given function is

$f(x,y)=c(x-y)$

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,

$\int\limits^3_{-2} \,\int\limits^2_0 {f(x,y)} \, dx dy\\=\int\limits^3_{-2} \,\int\limits^2_0 {c(x-y)} \, dx dy\\\\=\int\limits^3_{-2} \,[2c-2cy]dy\\=10c-5c\\=5c\\The integral should be1.\\So, 5c=1$

∴$c=\frac{1}{5}$

Therefore, the required value of c is 1/5.