The duration, TTT hours, for which a specialized solar cell generates its maximum power output during a laboratory test cycle is modeled by the probability density function
f(t)={2t270≤t≤k127(9−t)k<t≤90otherwise f(t) = \begin{cases} \frac{2t}{27} & 0 \le t \le k \\ \frac{1}{27}(9-t) & k < t \le 9 \\ 0 & \text{otherwise} \end{cases} f(t)=⎩⎨⎧272t271(9−t)00≤t≤kk<t≤9otherwiseShowing your working clearly, determine the value of the constant kkk.
State the mode of TTT.
Find P(T≤1.5∣T≤k)P\left( T \le 1.5 \mid T \le k \right)P(T≤1.5∣T≤k).
