COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 6)
1. Computer chips often contain surface imperfections. For a certain type of computer chip, the
probability mass function of the number of defects X is presented in the following table.
x
p(x)
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 7)
1) For continuous random variables X and Y with the joint probability density function,
f ( x, y ) x y 0 x 1,0 y 1
0 otherwise
a) Find X , Y , Var( X ) , Var(Y )
b) Find the covariance of X,
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 8)
1) In the past year there were 30 days on which accidents occurred along a certain stretch of
highway. Assume that the probability that an accident occurs on any one day is 30/365 and that
eac
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 9)
1).Suppose that the number of acorns that dropped onto the porch during the night is
Poisson distributed with parameter =2. Find (a) P(X=0), (b) P(X3), (c) P(X2),
and (d) P(X=0|X<2).
2). Let f
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 9)-answer
1).Suppose that the number of acorns that dropped onto the porch during the night is Poisson
distributed with parameter =2. Find (a) P(X=0), (b) P(X3), (c) P(X2), and (d) P(X=0|X<2).
So
OMP211 Data and System Modeling (PROB/STAT)
Tutorial answer (Week 11)
1. Suppose that a sample of n = 1,600 tires of the same type are obtained at random from an
ongoing production process in which 8% of all such tires produced are defective. What is the
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 12)
1.
A person arrives at a certain bus stop each morning. The waiting time, in minutes, for a bus to
arrive is uniformly distributed on the interval (0, 15).
(a)
(b)
Find the standard deviation
COMP 211 Data and System Modeling (Prob/Stat)
The Hong Kong Polytechnic University
Midterm Exam Answer (March 7, 2012)
Question 1:
Question 2:
Question 3:
a)
Given that
Therefore
occurs, there are 9 components remaining, of which 3 are defective.
.
. (4 m
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 2)
1) With the use of examples, explain the difference between sample statistics and population
parameter.
2)a) Discuss the difference between population variance and sample variance.
b) Consider
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 2) -Answer
1) With the use of examples, explain the difference between sample statistics and population
parameter.
Answer:
A population is the entire collection of objects or outcomes about which
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 6)
1.
a.
P( X 2) = 0.4+0.3+0.15=0.85
b.
P( X 1) = 0.15+0.10+0.05=0.3
c.
X = (00.4)+ (10.3)+(20.15)+(30.1)+(40.05)=1.1
d.
2
X 0 - 1.1 2 0.4 1 - 1.1 2 0.3 2 - 1.1 2 0.15 3 - 1.1 2 0.1 4 - 1.1 2 0
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 5) -Answer
1.
P(B|C) = P(BC)/P(C) = 0.0225 / 0.4 = 0.05625 P(B)
events B and C are not statistically independent
b.
2.
a.
P(A and C) = P(A) + P(C) - P(A or C)
= 0.21 + 0.40 - 0.40 = 0.21 0
even
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 7) Answer
1) For continuous random variables X and Y with the joint probability density function,
a) Find ,
b) Find the covariance of X, Y cov(X,Y) and the correlation coefficient of X and Y.
Ans
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 8) -Answer
1) In the past year there were 30 days on which accidents occurred along a certain stretch of
highway. Assume that the probability that an accident occurs on any one day is 30/365 and
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 10)
1. a) Suppose that the average household income in some country is 900 coins, and the
standard deviation is 200 coins. Assuming the Normal distribution of incomes,
compute the proportion of m
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 10) -Answer
1. a) Suppose that the average household income in some country is 900 coins, and the
standard deviation is 200 coins. Assuming the Normal distribution of incomes,
compute the proport
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 11)
1. Suppose that a sample of n = 1,600 tires of the same type are obtained at random from an
ongoing production process in which 8% of all such tires produced are defective. What is the
probab
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 12)
1.
A person arrives at a certain bus stop each morning. The waiting time, in minutes, for a bus to
arrive is uniformly distributed on the interval (0, 15).
(a)
(b)
Find the standard deviation
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 3) -Answer
1) a) Suppose a fair die is thrown once.
i) What is the sample space?
ii) What is P(number of dots=1)
iii) P(number of dots<5)?
Solution:
Sample space = cfw_1,2,3,4,5,6
P(number of dot
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 4)
1) Consider the experiment of drawing one card from a standard deck of 52 cards. Let A be the event
that a club is selected, let B be the event that a face card (jack, queen, or king) is drawn
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 4) -Answer
1) Consider the experiment of drawing one card from a standard deck of 52 cards. Let A be the event
that a club is selected, let B be the event that a face card (jack, queen, or king)
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 5)
1. Given that three events A, B, and C with probabilities:
P(A) = 0.21,
P(B) = 0.15,
P(B and C) = 0.0225,
P(C) = 0.40,
P(A or C) = 0.40,
a.
Are events B and C statistically independent?
b.
P(A
COMP211 Data and System Modeling (PROB/STAT)
Tutorial (Week 3)
1) a) Suppose a fair die is thrown once.
i) What is the sample space?
ii) What is P(number of dots=1)
iii) P(number of dots<5)?
b) Two dices are thrown. Let E be the event that the sum of the