AUniversity lecturer ends her lecture in a particular course she gives on Wednesdays between 11:00 a.m. and 11:04 a.m. Suppose that the time X (in minutes) between 11:00 a.m. and the end of the lecture has the following distribution function

for a positive constant c.We assume that the lecture finishes before 11:04 a.m. with probability one, i.e. P(X (i) What is the value of the constant c?
(ii) Find the probability that the lecture finishes

(a) before 11:03 a.m.,

(b) after 11:01 a.m.
(iii) Assuming that on a particular day the lecture has not finished by 11.01, what is the probability that it will finish within the next two minutes?

Transcribed Image Text:

0, t < 0, F(t)= ct, 1, 0