1)- Buses arrive at a specified stop at 15-minute intervals starting at 7 A.M. That is, they arrive at 7, 7:15, 7:30, 7:45, and so on. If a passenger arrives at the stop at a time that is uniformly distributed between 7 and 7:45, find the probability that he waits.

a. Less than 5 minutes for a bus.

b. At least 12 minutes for a bus.

2)- The current in a semiconductor diode is often measured by the Shockley equation = ( ) where V is the voltage across the diode; I0 is the reverse current; a is a

constant; and I is the resulting diode current. If a = 5, I0 = 106, and V is uniformly distributed over (1, 3). Find

a. E(I) b. Var(I)