Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n = 40 , p = 0.05 .

Question

Want to see the full answer?

Answer 1

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 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

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 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Answer 6

Chapter 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

Answer 7

Chapter 5.8, Problem C.2RE

a.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

Answer 8

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

Answer 9

b.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

Answer 10

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

Answer 11

c.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

Answer 12

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Answer 13

d.

To determine

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 17

Ch. 5.4 - What is the difference between a...Ch. 5.4 - Suppose a continuous random variable can only take...Ch. 5.4 - What is a standard normal distribution?Ch. 5.4 - (a) What is the area to the left of 0.2 under a...Ch. 5.4 - (a) What is z.30? What does it mean? (b) What is...Ch. 5.5 - What is the difference between a standard normal...Ch. 5.5 - What does the principle of standardization mean?Ch. 5.5 - Suppose the distribution of serum-cholesterol...Ch. 5.8 - Why do we use the normal approximation to the...Ch. 5.8 - Prob. C.2RE

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n = 40 , p = 0.05 .

Solution Summary: The author explains how the binomial distribution can be approximated by a normal distribution or Poisson distribution.

Concept explainers

Videos

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=40,p=0.05.

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=300,p=0.05.

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=500,p=0.001.

Check whether the binomial distribution can be approximated by a normal distribution or a Poisson distribution or both when n=1,000,p=0.001.

Want to see the full answer?

Chapter 5 Solutions