The mean and standard deviation of the sampling distribution of x ¯ 1

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Answer 1

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

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You have been hired as an intern to run analyses on the data and report the results back to Sarah; the five questions that Sarah needs you to address are given below. Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship. Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. (In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size). Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model. Interpret the…

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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)

Answer 2

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Expert Solution & Answer

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Expert Solution & Answer

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Answer 5

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Answer 6

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

Answer 7

Chapter 8.2, Problem 8.2LM

(a)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1

Answer 8

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

Answer 9

(b)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯2

Answer 10

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

Answer 11

(c)

To determine

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

Answer 12

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Answer 13

(d)

To determine

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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The mean and standard deviation of the sampling distribution of x ¯ 1

Solution Summary: The author explains that the mean value of sampling distribution of stackrel is 12 and the standard deviation is 0.5.

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To find: The mean and standard deviation of the sampling distribution of x¯1

To find: The mean and standard deviation of the sampling distribution of x¯2

To find: The mean and standard deviation of the sampling distribution of x¯1−x¯2 .

To check: Whether the statistic x¯1−x¯2 will be normally distributed or not.

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