Question
In: Statistics and Probability
Derive below Results 1 to 4 from Axioms 1 to 3 given in Section 2.1.2 in...
Derive below Results 1 to 4 from Axioms 1 to 3 given in Section 2.1.2 in the textbook.
Result 1: P(Ac)=1−P(A)
Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B)
Result 3: For any two events A and B, P(A) = P(A ∩ B) + P(A ∩ Bc)
Result 4: If B ⊂ A, then A ∩ B = B. Therefore, P(A) − P(B) = P(A
∩ Bc), and
P(A) ≥ P(B).
Solutions
orchestra answered 1 year agoRelated Solutions
Derive below Results 1 to 4 from Axioms 1 to 3. Axiom 1: P(A)≥ 0 Axiom...
Derive below Results 1 to 4 from Axioms 1 to 3.
Axiom 1: P(A)≥ 0
Axiom 2: P(S)=1
Axiom 3: If A and B are mutually exclusive events, then P(A ∪
B)= P(A)+P(B)
Result 1: P(Ac)=1−P(A)
Result 2: For any two events A and B, P (A∪B) = P (A)+P (B)−P
(A∩B)
Result 3: For any two events A and B, P(A) = P(A ∩ B) + P(A ∩
Bc)
Result 4: If B ⊂ A, then A ∩ B...
You are given the following results from a sample of five observations. 4 6 3 4...
You are given the following results from a sample of five
observations. 4 6 3 4 3
a. Construct a 99% confidence interval for the population
variance.
b. The null and alternative hypotheses are H0: σ2 ≥ 2 and Ha: σ2
< 2. Compute the test statistic.
c. Perform the test of the hypothesis at the 1% level.
d. What do you conclude about the population variance?
A researcher used cross-section data for the 10 areas to generate the results given below. Use...
A researcher used cross-section data for the 10 areas to generate
the results given below.
Use the regression results to estimate the following.
Be sure to show your calculations for each question
a) The estimate of Auto Sales for a population of 100.
b) The 95% confidence interval for the estimate of Auto Sales for a
population of 100.
c) The 95% confidence interval for the slope coefficient for the
population.
Area
Auto Sales
Population
1
185792
133.17
2
85643...
Given the matrix as shown below n_array = 3 1 8 3 5 7 4 9...
Given the matrix as shown below
n_array =
3 1 8
3 5 7
4 9 2
Write a M-file script program that generates this n_array, and
answer each question using one line of MATLAB statement.
a) Replace the second column of the n_array with a column of
0s
b) Replace the element in the second-row, third-column with a
zero
c) Change the n_array to a 4 x 3 array by adding a row of 0s
The end result for...
Introduction to business Section D Case study 4 Read the case given below thoroughly and answer...
Introduction to business
Section D
Case study 4
Read the case given below thoroughly and answer the
questions.
Sara has been working at a handicrafts factory for about two
years. One day she had a fight with her production supervisor
Nasser who is responsible for 50 workers under his supervision.
Nasser was under stress and found it very difficult to control
quality with this big number of workers. Sara made a mistake while
packaging the products so he shouted at...
1. Survey results on the Age and Marital Status of women are given below. Use the...
1. Survey results on the Age and Marital Status of women are
given below. Use the data to answer the questions.
AGE
18
to 24 25 to
64 65 and over total
Married
3,046
48,116
7,767
58,929
Never Married
9,289
9,252
768
19,309
Widowed
19
2,425
8,636
11,080
Divorced
260
8,916
1,091
10,267
total
12,614
68,709
18,262
99,585
A. What is the probability of a randomly selected woman being
Widowed?
B. What is the probability of a randomly selected woman...
1. Survey results on the Age and Marital Status of women are given below. Use the...
1. Survey results on the Age and Marital Status of women are
given below. Use the data to answer the questions.
AGE
18
to 24 25 to
64 65 and over total
Married
3,046
48,116
7,767
58,929
Never Married
9,289
9,252
768
19,309
Widowed
19
2,425
8,636
11,080
Divorced
260
8,916
1,091
10,267
total
12,614
68,709
18,262
99,585
A. What is the probability of a randomly selected woman being
Widowed?
B. What is the probability of a randomly selected woman...
Section 1 (3 marks: You can start this section after Week 4 lecture) Read the following...
Section 1 (3 marks: You can start this section after Week 4
lecture) Read the following article: Harford, T. (2014), ‘Big data:
A big mistake?’, Significance 11(5), 14–19. Question: Critically
evaluate the main points of the article using three bullet points,
in less than 150 words in total. Critical evaluation means • To
give your opinion on something • To support your opinion (with
evidence where possible). • Note: Critiquing is NOT simply stating
that something is “bad”. • Weigh...
The results of a tensile experiment on a metal is given in the table below. The...
The results of a tensile experiment on a metal is given in the
table below. The tensile sample had circular cross section with the
diameter of 10 mm and initial gauge length of 60 mm. Use this table
and calculate:
Force (N)
Measured Length (mm)
Region
0
60
Elastic
15708
60.15
Elastic
31416
60.3
Elastic
35343
60.6
Plastic
36128
61.2
Plastic
36914
63
Plastic
37306
66
Plastic
(a) The Young modulus of this metal (in GPa)
(b) The modulus of...
Monthly returns for two stocks are given below: Month 1 2 3 4 5 6 7...
Monthly returns for two stocks are given below:
Month
1
2
3
4
5
6
7
8
9
10
11
12
rA
4.10%
1.12%
1.66%
−0.18%
−4.71%
−0.60%
−0.91%
1.02%
1.69%
−0.51%
1.42%
2.52%
rB
−3.36%
−1.93%
−0.45%
0.34%
4.27%
8.48%
1.86%
4.10%
6.41%
−5.24%
−1.06%
1.40%
(a) Calculate the correlation between the returns of these two
stocks. Consider a portfolio of the two stocks weighted 60:40 at t
= 0.
(b) Calculate the returns on the rebalanced portfolio for...
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