Question: 1. Three people, A, B and C, live in the same neighborhood and use the same bus line to go to work. Each of the three has a probability of ¼ of making the 6:10 bus, a probability of ½ of making the 6:15 bus, and a probability of ¼ of making the 6:20 bus. Assuming independence, what is the probability that they all take the same bus?
2. The probability density function of a certain voltage is given by
pv(v) = ve-vU(v)
where U(v) is the unit step function.
(a) Sketch this probability density function.
(b) Sketch the distribution function of v.
(c) What is the probability that v is between I and 2?