Independence of RV

Probability Level 2

A certain joint probability density function is given by the formula

f X Y ( x y ) = π 2 x sin ⁡ ( x y ) , f_{XY} (xy) = \dfrac{\sqrt{\pi}}{2} x\sin (xy),

where x x and y y are drawn from the rectangle [ 0 , π ] × [ 0 , π ] . \big[0,\sqrt{\pi}\big]\times \big[0,\sqrt{\pi}\big].

Are the random variables X X and Y Y independent?

Yes No Maybe

Matt DeCross by Matt DeCross , 27, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Matt DeCross
Apr 20, 2016

Two random variables are independent if their joint probability density function factors into the marginal distributions. cos ⁡ ( x y ) \cos(xy) does not factor and therefore these random variables are not independent.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...