# Thread: Distribution function and Densities

1. ## Distribution function and Densities

These question seemed simple to me, however I believe I am getting confused between distribution functions and densities.

Question

Find the distribution function, and hence the density, of (1/x)

Any help would be great. The reason why im confused is because i thought 1/x was already a density, so why would it need to be found?

Thanks

2. Do you have an orginal distribution?
I can tranform any rv via 1/x, if I know what distributon we are starting with.
In other words.
Give me the density of X and I will give you the density of Y=1/X.

3. Yes it is a random variable, and I have been told that the range is from

0 < x < 2

Does this help?

4. nope
how about an f(x) or an F(x)?

5. OK, here is the complete question:-

X has density x/2 over 0 < x < 2, and 0 elsewhere. Sketch its density and distribution function. Find the distribution function, and hence the density, of X/2, e^X, 1/X, and |X - 1|.

So all I know is that it has something to do with random variables. Please dont explain all of them as that is time consuming, if you can do one then Im sure I can work out the rest with the same technique.

6. Originally Posted by ryanhorne
OK, here is the complete question:-

X has density x/2 over 0 < x < 2, and 0 elsewhere. Sketch its density and distribution function. Find the distribution function, and hence the density, of X/2, e^X, 1/X, and |X - 1|.

So all I know is that it has something to do with random variables. Please dont explain all of them as that is time consuming, if you can do one then Im sure I can work out the rest with the same technique.

that is just calculus one

Let Y=1/X

the density of Y is

$f_Y(y)=f_X(x)/y^2$ since we need the absolute value around the $-y^{-2}$

Thus $f_Y(y)={1\over 2y}y^{-2}={1\over 2y^3}$

for y>1/2

7. Just had a thought, do you reckon the final answer should have been negative?

8. Originally Posted by ryanhorne
Just had a thought, do you reckon the final answer should have been negative?

probabilities are never negative
same with probability functions

9. haha, good point.