Question 3. You are given a weighted sum of PDF(s) f1(x) and f2(x). Specifically, we have z(2) = WIfi(2) + w2.f2(20), a E (-00, 00). Obtain conditions that when satisfied by the scalar weights w1 and w2 ensure that z(x) is also a PDF. Question 4. A lecture is 60 minutes long. You arrive at the beginning of the lecture. The process of recording attendance is completed by a certain time selected uniformly and randomly during the lecture. You leave soon after attendance is recorded. Calculate the expected value of the time you spend attending the lecture