sneaky666
Oct30-10, 03:32 PM
1. The problem statement, all variables and given/known data
For each of the following c.d.f F, find a formula for X in terms of U, such that if U~Uniform[0,1], then X has c.d.f F.
a)
F(x) =
0 if 0 x<0
x if 0<=x<=1
1 if x>1
b)
F(x) =
0 if 0 x<0
x^2 if 0<=x<=1
1 if x>1
c)
F(x) =
0 if 0 x<0
(x^2)/9 if 0<=x<=3
1 if x>3
How do I solve these?
2. Relevant equations
3. The attempt at a solution
a)
Is it
Y=min(x:F(x)>=u)
Do i need to simplify this more?
For each of the following c.d.f F, find a formula for X in terms of U, such that if U~Uniform[0,1], then X has c.d.f F.
a)
F(x) =
0 if 0 x<0
x if 0<=x<=1
1 if x>1
b)
F(x) =
0 if 0 x<0
x^2 if 0<=x<=1
1 if x>1
c)
F(x) =
0 if 0 x<0
(x^2)/9 if 0<=x<=3
1 if x>3
How do I solve these?
2. Relevant equations
3. The attempt at a solution
a)
Is it
Y=min(x:F(x)>=u)
Do i need to simplify this more?