EE126, Fall 2000
Midterm #1
Professor Chang-Hasnain
Problem #1 (20 pts)
Given P[A|B] = a
   P[B] = b
   P[(B^c)|(A^c)] = e
Express P[B|A] in terms of a, b, e.
Problem #2 (20 pts)
A telephone transmission system typically consists of an equipment called a multiplexer, which is capable of
multiplexing M active phone lines at a given time. Consider an active phone line transmits 1 packet per fixed
time period T, and an inactive phone line, 0 packet per T.
Consider an apartment complex with 48 phone lines; the probability of each line transmitting signal is p, and
not transmitting signal is 1-p, where p = 1/3. Let X be the number of packets transmitted per T, and X is a
binomial random variable.
(Hint: P[X=k] = {n!/[(n-k)!k!]}*( p^k)*[(1-p)^(n-k)])
(a) (6 pts) Write down the expressions of the pdf and cdf of X
(b) (7 pts) What is P[X>24] ? Express this in formula; you don't need to provide numeric value.
(c) (7 pts) If this apartment decides to use an M-line multiplexer for its transmission system and M
(Hint: fraction of lost packes = number of discarded packets/total number of packets produced)
Problem #3 (20 pts)
A biased coin is tossed. What is the probability that you have to flip it exactly 8 times to see exactly 3 heads?
P(Heads)=0.6.
Problem #4 (20 pts)
There are 5 accidents/month on a highway. Accidents on this highway are distributed as a Poisson random
variable. Find the probability there will be no accidents in a given year.
Problem #5 (20 pts)
Tom and Paul roll (2) dice alternatively starting with Tom. Consider they use two fair 6-faced dice. The
player who rolls 6 first wins. They continue to roll until one of them wins. Find the probability that Tom
wins.
EE126, Midterm #1, Fall 2000
EE126, Fall 2000Midterm #1 Professor Chang-Hasnain 1
