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Question about simlating exponential r.v.s watch

1. How do I construct the inverse of 2x-5t?
2. What have you tried so far?
3. What I've tried is to construct the inverse of the exponential to give a new pdf, but I can't get the inverse...
4. First find the c.d.f. F for f(x). That is, find p(X <= x).

Then if Y is unif(0,1), has the same distribution as X.
5. (Original post by DFranklin)
First find the c.d.f. F for f(x). That is, find p(X <= x).

Then if Y is unif(0,1), has the same distribution as X.
So I'm to integrate it first... got it.
6. (Original post by DFranklin)
First find the c.d.f. F for f(x). That is, find p(X <= x).

Then if Y is unif(0,1), has the same distribution as X.
I've got the integral as F(x)=-exp(-x^3), but I can't find the inverse of it. Help?
7. Well, what's the inverse of exp?
8. (Original post by DFranklin)
Well, what's the inverse of exp?
This is where I get stuck:

U = -exp(-x^3)
-U =exp(-x^3)
ln(-U) = -x^3
-ln(-U) = x^3
cube root of (-ln(-U)) = x

But this looks nothing like other examples I've covered, in which x is usually ln(1-U) or something simple
9. Check your arbitrary constant (from when you integrated). What is P(X<=infinty) going to be?
10. (Original post by DFranklin)
Check your arbitrary constant (from when you integrated). What is P(X<=infinty) going to be?
Sorry, I don't understand When I put the limits 0 and infinite in, the integral works out as 1.
11. Who said anything about limits (definite integral limits, at any rate)?

By definition, F(x) = P(X <= x).

Since doesn't tend to 1 as , you have a (easily remedied) problem...
12. (Original post by DFranklin)
Who said anything about limits (definite integral limits, at any rate)?

By definition, F(x) = P(X <= x).

Since doesn't tend to 1 as , you have a (easily remedied) problem...
Oh! Is it to change it to ?
13. Yes. After that, your method should be OK, I think.
14. (Original post by DFranklin)
Yes. After that, your method should be OK, I think.
Oh. Huge thanks for helping me through this question step-by-step.

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