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

Could you please give the solution? enter image description here

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    $\begingroup$ (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. $\endgroup$
    – gunes
    May 31 '20 at 16:59
  • $\begingroup$ @gunes Thanks - I tried this but am not sure I understand as it didn't work. Would you mind showing me the solution? $\endgroup$
    – Fab
    May 31 '20 at 17:41
  • $\begingroup$ Why don’t you share yours and we can help you get unstuck. $\endgroup$
    – gunes
    May 31 '20 at 17:46
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    $\begingroup$ thanks again @gunes I added some things I tried as another pic in the question $\endgroup$
    – Fab
    May 31 '20 at 17:52
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Some hints:

(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.

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