Sketch the distribution of the variable x.

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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 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

b.

To determine

Obtain the standardized version z of x.

c.

To determine

Sketch the distribution of z.

d.

To determine

Fill in the given blank.

e.

To determine

Fill in the given blank.

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Problem 3. Pricing a multi-stock option the Margrabe formula The purpose of this problem is to price a swap option in a 2-stock model, similarly as what we did in the example in the lectures. We consider a two-dimensional Brownian motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices are modeled by the following equations: dX = dY₁ = X₁ (rdt+ rdt+0₁dW!) (²)), Y₁ (rdt+dW+0zdW!"), with Xo xo and Yo =yo. This corresponds to the multi-stock model studied in class, but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure P is already the risk-neutral measure (Both stocks have rate of return r). We write σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to exchange one share of X for one share of Y. That is, the option has payoff F=(Yr-XT). (a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for the process Xt. Reminder before proceeding to question (b): Girsanov's theorem…

Problem 1. Multi-stock model We consider a 2-stock model similar to the one studied in class. Namely, we consider = S(1) S(2) = S(¹) exp (σ1B(1) + (M1 - 0/1 ) S(²) exp (02B(2) + (H₂- M2 where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with t≥0 Cov (B(¹), B(2)) = p min{t, s}. " The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian motion (W+)+20 (W(1), W(2))+20 such that = S(1) S(2) = = S(¹) exp (011W(¹) + (μ₁ - 01/1) t) 롱) S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t). where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p). Hint: The constants will follow the formulas developed in the lectures. (a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2) functions of (B(1), B(²)). as (b) Using the formulas obtained in (a), show that the process (WA) is actually a 2- dimensional standard Brownian motion (i.e. show that each component is normal, with mean 0, variance t, and that their…

The scores of 8 students on the midterm exam and final exam were as follows. Student Midterm Final Anderson 98 89 Bailey 88 74 Cruz 87 97 DeSana 85 79 Erickson 85 94 Francis 83 71 Gray 74 98 Harris 70 91 Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary. Test statistic: rs =

Answer 2

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 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

b.

To determine

Obtain the standardized version z of x.

c.

To determine

Sketch the distribution of z.

d.

To determine

Fill in the given blank.

e.

To determine

Fill in the given blank.

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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 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

b.

To determine

Obtain the standardized version z of x.

c.

To determine

Sketch the distribution of z.

d.

To determine

Fill in the given blank.

e.

To determine

Fill in the given blank.

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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 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

b.

To determine

Obtain the standardized version z of x.

c.

To determine

Sketch the distribution of z.

d.

To determine

Fill in the given blank.

e.

To determine

Fill in the given blank.

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Answer 5

Chapter 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

b.

To determine

Obtain the standardized version z of x.

c.

To determine

Sketch the distribution of z.

d.

To determine

Fill in the given blank.

e.

To determine

Fill in the given blank.

Answer 6

Chapter 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

Answer 7

Chapter 6.1, Problem 40E

a.

To determine

Sketch the distribution of the variable x.

Answer 8

b.

To determine

Obtain the standardized version z of x.

Answer 9

b.

To determine

Obtain the standardized version z of x.

Answer 10

c.

To determine

Sketch the distribution of z.

Answer 11

c.

To determine

Sketch the distribution of z.

Answer 12

d.

To determine

Fill in the given blank.

Answer 13

d.

To determine

Fill in the given blank.

Answer 14

e.

To determine

Fill in the given blank.

Answer 15

e.

To determine

Fill in the given blank.

Answer 16

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Answer 17

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Answer 18

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Answer 19

Ch. 6.1 - What is a density curve?Ch. 6.1 - State the two basic properties of every density...Ch. 6.1 - For a variable with a density curve, what is the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...Ch. 6.1 - In each of Exercises 6.46.11, assume that the...

Sketch the distribution of the variable x.

Solution Summary: The author calculates the distribution of the variable x using the MINITAB software: Choose Graph > Probability Distribution Plot > OK.

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Sketch the distribution of the variable x.

Obtain the standardized version z of x.

Sketch the distribution of z.

Fill in the given blank.

Fill in the given blank.

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