Section 2: Probability Theory and Random Processes
ECE 316

Spring 2008
Problems
1. (a) How manyI dierent 7plaoe license plates are possible if the rst 2 places are for letters
and other 5 for numbers?
Solution. By the generalized version of the basic principle the answer is
26261010101010=67,500,000
(b) Repeat part (a
Section 2: Probability Theory and Random Processes
ECE 316

Spring 2008
Mm 170 mm
m M2 159 if Miter), W55 403 Mai @5112) 4 33 Me ME,
lpis am Mkh a W 9 at/Lt Wows 3W be
_._LL,'_._. _
41(442! 339,65?
6% {9), mm raftPcbzin/ we m W? a?) Meat WNW.
NW/ am. am Asgard 'a (MFAWE iii 4% {3L (#6th whim/5 wiin 1% @4th
M2 Wmmr Mau 5;
Section 2: Probability Theory and Random Processes
ECE 316

Spring 2008
Problems
1. Two fair dice we miied. Find the joint pivbubiiy mass meiion of X and V when
(a) X is the Imyesi value obtained an any die and Y is the sum a] the wines.
Solution. (3.) The joint mass function of X and V1 p[i1j} = P[X = LY = can be
omnputenl
Section 2: Probability Theory and Random Processes
ECE 316

Spring 2008
Problems
3. FIX and Y two independent uniform {0,1} random ohrs'ohtes, show that
2
{o+1)[os+2} for a} 0'
Er
X _ ylral =
Solution. From the denition of the expectation, we hove
I. I.
XY*]=L A Ixeldeds.
Next, we compute the inner integration as foUcuws: