A geometric problem about statistics

Probability Level 3

Let a random variable $(X,Y)$ having a constant ( $k$ ) density function :

$f(x,y) = k$ in the region $\{(x,y) \in \mathbb{R}^2; y > 0, \space x + y > 1, \space x + 2y < 2\}$ and

$f(x,y) = 0$ for the rest of points in $\mathbb{R}^2$ .

Find and submit $k$

1 solution

Guillermo Templado
Aug 29, 2016

$1 = \iint_{\mathbb{R}^2} f(x,y) dxdy = k \cdot \text{ area } \Delta ABC = k\frac{1}{2}\Rightarrow k = 2$

I have also done this in same way but I have a question.If here f(x,y) becomes a variable in stead of constant k.Then how it can be done ????

Kushal Bose - 4 years, 9 months ago

I recommended ,try part I if you mean f(x,y) is not constant

Guillermo Templado - 4 years, 9 months ago