Fall 2016
STAT2001 Midterm Examination
Instructions: It is a 1.5-hour Exam. Do all six questions. Show your steps clearly.
Give the best answer to each question.
Question 1:
Suppose that in a hospital
Solution to assignment 2 2015
1.
P(X=1)= 0.6*0.3+0.7*0.4=0.46
P(X=2)=0.6*0.7=0.42
P(X=0)=0.4*0.3=0.12
EX=1*0.46+2*0.42=1.3
2.
Let X be the daily demand. X~b(9,1/2)
Case 1 mother
The profit
Y=4x-12(5-x
STAT2001 Assignment 1
Do all 8 questions.
Deadline for this assignment is 2nd October 5:00p.m. You can submit to the
assignment locker (next to LSB 125) or to the Teaching Assistants directly.
1.
From
STAT2001 Assignment 2
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 23rd Oct. 5:00p.m. You can submit to the assignment locker
(next to LSB 125) or to your Tutors.
1. Tw
STAT2001 Assignment 3
Do all 8 questions. Show your steps clearly.
Deadline for this assignment is 13th Nov. 5:00p.m. You can submit to the assignment locker
(next to LSB 125) or to your Tutors.
1. Le
STAT2001 Assignment 4
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 27th Nov. 5:00p.m. You can submit to the assignment
locker (next to LSB 125) or to your Tutors.
1.
A
STAT2001 Assignment 5
Do all 6 questions. Show your steps clearly.
Deadline for this assignment is 4th Dec. 5:00p.m. You can submit to the assignment
locker (next to LSB 125) or to the elearning syste
STA2001 Tutorial Notes 2
1.Prove or give counterexamples to the following statements:
(a)If A is independent of B, then A is independent of B.
(b)If A is independent of B, and B is independent of C, t
STA2001 A/B
Tutorial 10
1. Useful Identities: (1) E[ X ] = E[ E[ X | Y ]
(2) Var[ X ] = Var[ E[ X | Y ] + E[Var[ X | Y ]
Example: Customers arrive at the automatic teller machine in accordance with
a
STA 2001 Tutorial 8 Solution
Example 1: Let X have the p.d.f. f ( x) =
3 2
x
35
2 < x < 3 . Find the
p.d.f. of Y = ( X + 1) 2 .
The support of Y is 0 < y < 16 . Moreover, for 0 < y < 1 we have two in
Tutorial 7
2/11/2005, 4/11/2005
Continuous Distribution:
The probability density function (p.d.f.) of the continuous random variable X with
space S is an integrable function f(x) satisfying the follow
Tutorial 11
30/11/2005, 1/12/2005
Example 1:
Let Z1, Z2, , Z7 be a random sample from the standard normal distribution N(0,1).
Let W = Z 12 + Z 22 + . + Z 72 . Find P(1.69<W<14.07).
Solution:
W = Z 12
STA2001 Basic Concepts in Statistics and Probability I
TUTORIAL 9
16/18 NOV 2005
Correlation and Conditional Distribution
Example 1
Let X be a random variable with the following probability mass funct
5/7 OCT 2005
STA 2001 Tutorial 4
1. Suppose the annual incomes in thousands of dollars for the Edwards, Francis,
Gray, Harris, and Icklar families are 30,35,30,25 and 35, respectively. Two
families ar
5/7 OCT 2005
STA 2001 Tutorial 4
1. Suppose the annual incomes in thousands of dollars for the Edwards, Francis, Gray,
Harris, and Icklar families are 30,35,30,25 and 35, respectively. Two families ar
Solution to assignment 3 2015
1.
(a)
1
)
3
x 3
3
1
f ( x )dx (5 x 2 ) dx (5 x x 3 ),0 x 1
0 14
14
3
1
So c=3/14
(b)
1
0
0
1 f ( x)dx c(5 x 2 )dx c(5
x
F ( x)
x<0
=1,
(c)
0.082
x>1
1
1 3
27
E ( X ) x
Solution for STAT2001 2016 Midterm
1. (a) Let X1 denote the number of babies born during next 5 hours, then
X1 P oisson(1 ), 1 =
5
3 = 0.625
24
expect no. of birth in 5 hours
So,
P (X1 2) = P (X1 = 0
STAT2001 Assignment 3
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 8th Nov. 5:00p.m. You can submit to the assignment
locker (next to LSB 125) or submit on Blackboard s
STAT2001 2017 Midterm Solution
1(a) For a Poisson process with rate 5 per day. For a period of 5 hours, the number of births (X)
follow poisson(5*5/24)=Poisson(25/24). P(X2)=1-P(X=0)-P(X=1)=1-exp(-25/
Solution of Assignment 1:
6 6 6
1 (a) Number of choices = 36
5
4
4
6 6
(b) Number of choices = 26
3
5
2.
Let A denotes the event of buy suit, B denotes buy shirt, C denotes buy tie.
P( A) 0.22,
STAT2001 Assignment 4
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 17th Nov. 5:00p.m. You can submit to the assignment
locker (next to LSB 125) or submit on Blackboard
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Course Exami
1, An example for Gamma distribution:
Phone calls arrive at a mean rate of = 4 per minute according to Poisson Process.
Let W be the waiting time in minutes until the second call, what is the distribu
2nd Supplementary notes for Ch.1
1. On
P.30,
example that pairwise independence cannot imply
. How about the other way around, that is whether the
P( A B C ) P ( A) P ( B ) P (C )
condition
we
give
an
STAT 2001 Assignment 1
Name: WEI Jiarui
SID:1155091746
1. a. There are a total of 8C5=56 choices without considering special situations.
If the feuding two are unfortunately invited simultaneously, th
Example of distribution of two continuous random variables
Letthejointp.d.f. ofXand Ybe f(x,y) =%x2(1h|yl), -1<x<1. -1<y<1.
(a) What is F(0.5,0.5)=P(XSO.5,YSO.5)?
(b) What are the marginal p.d.f. of
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Course Examination l51 Te
If you have taken a first statistics course, you may have learnt t-test, t-statistics. Indeed, a
random variable following a t-distribution having the following p.d.f.:
1
The above derivation is based
Appendix
Arithmetic Sequence
General term T(n):
a + (n-1) d
Summation of n terms S(n):
n
[2 a+ ( n1 ) d ] or
2
n
[ T ( 1 ) +T ( n ) ]
2
Geometric Sequence
General term T(n):
a r n1
Summation of n ter
Applications of Hypergeometric distribution:
1, Acceptance sampling:
Consider a buyer that buys machine parts in lots. A lot contains 25 items. An item can be
either defective or acceptable. Now if he
Solution to assignment 2:
1.
P(X=1)= 0.4*0.7+0.6*0.3=0.46
P(X=0)=0.6*0.7=0.42
P(X=2)=0.4*0.3=0.12
EX=1*0.46+2*0.12=0.7
2.
Let X be the daily demand. X~b(10,1/3)
Case 1 mother
The profit
Y=16X-12*6 ,X<
The derivations for example 17 on the lecture notes involve more mathematical steps. It is possible that
some of you may not be able to copy all steps. Therefore I type this note as supplementary. The
STAT2001 Assignment 2
Do all 7 questions. Show your steps clearly.
Deadline for this assignment is 20th Oct. 5:00p.m. You can submit to the assignment locker (next
to LSB 125) or submit on Blackboard