"If X is U(a,b), find the values of c and d in terms of a and b such that P(X < d)
= 0.75 where a < d < b.
P (c < X) = 0.9 where a < c < b"
I'm confused as to what formula to use or how to set this problem up. Any hints?
I know the pdf is 1/b-a. Should I be taking the integral of this from a to d etc?
Recall that if $a\leqslant x\leqslant b$ then $\mathbb P(X<x) = \frac{x-a}{b-a}$. So if $\mathbb P(X<d) = \frac34$ then $$ \frac{d-a}{b-a} = \frac34 \implies d = \frac34(b-a) + a. $$
The other case is similar, just using $\mathbb P(X>x) = 1 - \frac{x-a}{b-a}$.