=========================preview======================
(ELEC210)[2009](s)midterm~ee_swcaa^_10293.pdf
Back to ELEC210 Login to download
======================================================
13 March 2008 Bertram Shi
ELEC 210
Probability and Random Proceses in Engineering
Midterm Exam


Name: Student ID:
Seat No.:


show all your work




Give numerical answers to all problems. Fractions and mixed fractions are OK. Any approximations should be given to 3 significant digits.


Question Total Score
1 15
2 15
3 13
4 12
5 5
60

1. Suppose that customers service requests to a bank teller are one of three types: withdrawl, deposit or transfer. Assume that service requests from different customers are independent, that each customer only makes one service request, and that requests are made sequentially (one after the other). Assume also that the probability of different service requests are given by
P[withdrawl] = pW = 0.5 P[deposit] = pd = 0.4 P[transfer] = pt = 0.1
(a)
What is the probability that the first two customers both request withdrawls, the third a deposit and the fourth a transfer?

(b)
Find the conditional probablity that the fifth customer requests a withdrawl, given that the first four cus-tomers all requested transfers.


(c) What is the probability that among the first 5 customers, exactly 2 request deposits?
(d) What is the probability that the first transfer request comes from the 6th customer?
(e) What is the expected value and the variance of the number of customers that either request withdrawls

or transfers among the first 20 customers?

2. Suppose that a discrete random variable X takes integer values with probability mass k pXk()
1 515
2 415
3 315
4 215
5 115

3. Suppose that a bus arrives at a bus stop at time 7:X, where X is a continuous random variable with the function () that is zero except for at the values shown in the table. probablity density function as shown below.
pX k

.
1 1
.

(a) Find the probability of the event {2 <X 4}.
-------
x if 0 <x 1515
.
152
.fX x.21
()= ------C --------x if 15 <<x 30
.
.15 152 15 30
.
0 otherwise
.
(a) What is the probability that the bus arrives at 7:15?

(b) Find the expected value of X .
(b) What is the probability that the bus arrives before 7:05?

(c) Find the variance of X .
(c) What is the conditional probability that you have to wait more than five minutes if you arrive at the bus stop at 7:10 and the bus has not arrived yet?

(d) Find the expected value of (X +1)2. 4. Suppose that you are picking candies from a bowl while watching movie. In the bowl there are 30 lime fla-(d) What is the probablity that all of the orange candies have been eaten within the first 40 picks. By
P4

vored candies, 17 lemon flavored candies and 3 orange flavored candies. Suppose that the movie theatre is
within, we mean that the event includes the outcomes where the last orange candy is eaten on the 40th pick,

dark, so that you are picking candies at random. Suppose also that after you pick a candy from the bowl you
but that the l