# Math Help - F-distribution problem

1. ## F-distribution problem

2. $c\biggl({\bigl({X-1}\bigr)^2+\bigl({Y-2}\bigr)^2\over \bigl({Z-3}\bigr)^2}\biggr)$

$=\biggl({8\over 9}\biggl)\cdot {\biggl(\bigl({X-1\over 2}\bigr)^2+\bigl({Y-2\over 2}\bigr)^2\biggr)/2\over \bigl({Z-3\over 3}\bigr)^2/1}$

Where ${\biggl(\bigl({X-1\over 2}\bigr)^2+\bigl({Y-2\over 2}\bigr)^2\biggr)/2\over \bigl({Z-3\over 3}\bigr)^2/1}$ is an $F_{2,1}$

Because each of those are squares of standard normals, which is a chi-square with one df.

so c=9/8 I believe.