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.