How to generate a random variable by composition?

Asked Dec 02 '15 at 11:54

Active Dec 03 '15 at 10:47

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If I want to generate a random variable with such a pdf: $f(x) = \dfrac 3 {2}x^2 : [-1, 1] \to \Bbb R$ by composition, what should I do?

I think I can divide the pdf by $x=0$ into two parts. But the $f(x)$ of the new two parts are the same and the CDF of the left part can be a negitive value. But I have to use composition for its my homework. How can I do?

edited Dec 03 '15 at 10:47

asked Dec 02 '15 at 11:54

周庆特

1

Compute cdf $F$, generate a standard uniform $U$ and output $F^{-1}(U)$. – A.S. Dec 02 '15 at 12:44
I know that inverse transform method. But the homework says i have to use composition to do that. – 周庆特 Dec 02 '15 at 12:46
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It's unclear what "composition" means in this case. You could first generate $|x|$ and then flip a coin to determine the sign of $x$. – A.S. Dec 02 '15 at 12:48
Composition is also a method to generate random variates. – 周庆特 Dec 02 '15 at 12:53
How can I do?？？ – 周庆特 Dec 03 '15 at 10:46

How to generate a random variable by composition?

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