A continuous random variable XXX has probability density function
f(x)={c x(3−x),0≤x≤30,otherwisef(x) = \begin{cases} c\,x(3 - x), & 0 \le x \le 3 \\[4pt] 0, & \text{otherwise} \end{cases}f(x)={cx(3−x),0,0≤x≤3otherwise
for some constant ccc.
Find ccc, then compute P(1≤X≤2)P(1 \le X \le 2)P(1≤X≤2).
Select all that apply.
c=118c = \dfrac{1}{18}c=181 and P(1≤X≤2)=1027P(1 \le X \le 2) = \dfrac{10}{27}P(1≤X≤2)=2710
c=29c = \dfrac{2}{9}c=92 and P(1≤X≤2)=136P(1 \le X \le 2) = \dfrac{13}{6}P(1≤X≤2)=613
c=29c = \dfrac{2}{9}c=92 and P(1≤X≤2)=2027P(1 \le X \le 2) = \dfrac{20}{27}P(1≤X≤2)=2720
c=29c = \dfrac{2}{9}c=92 and P(1≤X≤2)=1327P(1 \le X \le 2) = \dfrac{13}{27}P(1≤X≤2)=2713