# How do you work with a function of a uniform distribution? [closed]

I am struggling with parts b and c. How do you solve them?

Could you please give the solution?

• (b) Try to find $F_X(x)$ and differentiate. (c) you just create random samples of $x$ and plot pdf, cdf etc and compare them to theoretical distribution. May 31 '20 at 16:59
• @gunes Thanks - I tried this but am not sure I understand as it didn't work. Would you mind showing me the solution?
– Fab
May 31 '20 at 17:41
• Why don’t you share yours and we can help you get unstuck. May 31 '20 at 17:46
• thanks again @gunes I added some things I tried as another pic in the question
– Fab
May 31 '20 at 17:52

(b) Find $$F_X(x)=P(X\leq x)=P(b/U^{1/a}\leq x)=P(U\geq b^a/x^a)$$. Take it from here, find $$F_X(x)$$, and then differentiate wrt $$x$$ to find the PDF.
(c) Pick some $$a,b$$ of your choice, and using any programming language you like, create several uniform random variables, for each uniform random, calculate $$X=b/U^{1/a}$$ and get random $$X$$'s. Plot a normalized histogram, overlay the theoretical PDF and comment on it.