# Homework Help: Density function question

1. Feb 2, 2010

### nhrock3

$$Y-U(-2\pi,2\pi)$$
find the density function of z=tan(Y)
?

X-U(0,1)
find the density function of W=a+bx
the solution is
W-U(a,a+b)

how to solve the first question ??

2. Feb 2, 2010

### HallsofIvy

I think that you are saying that uniformly distributed between $-2\pi$ and $and [itex]2\pi$, but I have to guess that bcause you didn't even say this was a probability question!

What have you done? You know that you are to show what efforts you have already made don't you?

What is the density function for Y?

3. Feb 2, 2010

### nhrock3

it is probability question

the density function of Y is distributed evenly
$$Y-U(-2\pi,2\pi)$$

i tried to solve it like the example question i showed

but here in tangense i have no idea
because i could find teh density by this
(tan(-2pi),tan(2p))
but this is wrong because if we have an interval mutiplication streches it
subtraction moves it to the left
but tangense
i have no idea

4. Feb 2, 2010

### HallsofIvy

Since Y itself is uniformly distributed from $-2\pi$ to $2\pi$, its cumulative probability function is $x/(2\pi)$ an its density function is the constant $dY/dx= 1/(2\pi)$. The density function of Z= tan(Y) is the derivative of tan(Y): $d(tan(x/(2\pi))$.

5. Feb 2, 2010

### nhrock3

you said facts but how you get to them?
the final solution is
$$f_z(t)\frac{1}{\pi(1+t^2)}$$
so its like you said

but i cant see a logical way like in the solved example i showed
?