# continuous random variable help?

• Nov 22nd 2009, 03:41 PM
Intsecxtanx
continuous random variable help?
The monthly profit of Company I can be modeled by a continuous random variable with density function f . Company II has a monthly …profit that is twice that of Company I. Determine the probability density function of the monthly profit of Company II.

a) (1/2) * f(x / 2)
b) f(x / 2)
c) 2 * f(x / 2)
d) 2 * f(x)
e) 2 * f(2x)

so far for a, I have

Let Company-I profit be Y and that of Company-II be X. Then X = 2Y, or Y=X/2, dY=dX/2 so that

f(y)dy = f(x/2)dx/2.

but I'm not sure if that makes sense? can anyone shed some light? thanks in advance.
• Nov 23rd 2009, 01:53 AM
mr fantastic
Quote:

Originally Posted by Intsecxtanx
The monthly profit of Company I can be modeled by a continuous random variable with density function f . Company II has a monthly …profit that is twice that of Company I. Determine the probability density function of the monthly profit of Company II.

a) (1/2) * f(x / 2)
b) f(x / 2)
c) 2 * f(x / 2)
d) 2 * f(x)
e) 2 * f(2x)

so far for a, I have

Let Company-I profit be Y and that of Company-II be X. Then X = 2Y, or Y=X/2, dY=dX/2 so that

f(y)dy = f(x/2)dx/2.

but I'm not sure if that makes sense? can anyone shed some light? thanks in advance.

$x = 2y \Rightarrow y = \frac{x}{2}$.

Therefore $f_X = f_Y(y) \cdot \left| \frac{dy}{dx}\right| = \frac{1}{2} f\left( \frac{x}{2}\right)$.