Alethia models the length of time, in minutes, by which her train is late on any day by the random variable $$\(X\)$$ with probability density function given by $$\( f(x)= \begin{cases}\frac{3}{8000}(x-20)^{2} & 0 \leqslant x \leqslant 20 \\ 0 & \text { otherwise. }\end{cases} \)$$ State one way in which Alethia's model may be unrealistic. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No:9709_s21_qp_63 Year:2021 Question No:6(d)
Answer:
Doesn't allow for trains \(>20\) mins late or Doesn't allow for trains being early
Knowledge points:
6.3.1 understand the concept of a continuous random variable, and recall and use properties of a probability density function (For density functions defined over a single interval only; the domain may be infinite,.)
Solution:
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