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4. Show the PDF and CDF of two-parameters of Weibull distribution (1) Use MATLAB to plot...
The Weibull distribution was introduced in Sect. 3.5. (a) Find the inverse cdf for the Weibull...
The Weibull distribution was introduced in Sect. 3.5. (a) Find the inverse cdf for the Weibull distribution. (b) Write a program to simulate n values from a Weibull distribution. Your program should have three inputs: the desired number of simulated values n and the two parameters α and β. It should have a single output: an n x 1 vector of simulated values. (c) Use your program from part (b) to simulate 10,000 values from a Weibull(4, 6) distribution and...
2. Find the mean and standard deviation of the hypergeometric distribution with the parameters n=3, a=4,...
2. Find the mean and standard deviation of the hypergeometric distribution with the parameters n=3, a=4, and N=8 (a) By first calculating the necessary probabilities to get the hypergeometric distribution (20 points) (b) Use the general formulas and calculate the mean and standard deviation using the original equations; (10points) (c) By using the special formulas for the mean and the variance of a hypergeometric distribution (10points)
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into...
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB > cdf; SUBC 〉 poisson 15. Find PX 〈 10)-[3] and P(15 X 20)= [3] 4. Suppose that Y has a hypergeometric distribution with parameters N = 20, M = 6, and n = 4, Use the command MTB > cdf 3; hypergeometric 20 6 4. a. [3] to find P(Y 53) = b. 3) Use the similar command to find P(Y > 2)...
Answer True or False for the following questions: 1. The probability density function (pdf) is used...
Answer True or False for the following questions: 1. The probability density function (pdf) is used to describe probabilities for continuous random variables. 2. The cumulative distribution function (cdf) gives the probability as an area. 3. The amount of time (beginning now) until an earthquake occurs has an uniform distribution 4. Normal distributions are commonly used in calculations of product reliability, or the length of time a product lasts. 6. The exponential distribution has the decay parameter, which says that...
3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist. & derive it. 4. X-i ~ cont with pdf fi(x) and CDF Fi(x), i=1, 2, , k....
3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist. & derive it. 4. X-i ~ cont with pdf fi(x) and CDF Fi(x), i=1, 2, , k. all independent. Define YjaFi(Xi), i=1, , k. Derive the distribution of
3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist....
1 Program 2-paramter Weibull distribution with β 100 rows by copying down the equation from Table...
1 Program 2-paramter Weibull distribution with β 100 rows by copying down the equation from Table 4.1. In the next column generate 1000 rows and in the next column 10 000 rows. Calculate the mean and standard deviation for each column. By hitting Recalculate' (typically F9) observe the mean and standard deviation values. What can you say about the variation for each group? 3.0 and η 000 into Excel spreadsheet and generate 2. When simulating the function Z-X where X...
Question 3 A more general form of Cauchy distribution is defined by the density function f(x;...
Question 3 A more general form of Cauchy distribution is defined by the density function f(x; m, 7) = where m is the location parameter, is the scale parameter and they are both constants. We will create a function to simulate draws of a Cauchy(m, 7) distribution in this exercise using the inversion method. (a) (4 points) Derive the cdf, and the inverse function of cdf for Cauchy(m, n). Describe a procedure to generate independent observations from a Cauchy(m, 7)...
Problem 2. The annual maximum wind speed in a location in the United States has the...
Problem 2. The annual maximum wind speed in a location in the United States has the Type II Largest Value distribution with mean 65 km/hr and standard deviation 20 km/hr. (a) Determine the parameters of the distribution and make a plot of the PDF. (b) What is the probability that the threshold of 100 km/hr will be exceeded in 10 years?
Now let's try a normal distribution. The first plot will be easy, but the second will...
Now let's try a normal distribution. The first plot will be easy, but the second will be more difficult to do, so follow the instructions carefully. First we'll plot a standard normal, then we'll see what happens if you change the parameters. x <- seq (-3.291, 3.291, length.out=100) gives us 100 equally spaced values of x between -3.291 and 3.291. “seq” let's us generate a sequence of numbers, and “length.out” tells us how many numbers we want in the sequence....
2. Find the mean and standard deviation of the hypergeometric distribution with the parameters n=3, a=4, and N=8 (a) By first calculating the necessary probabilities to get the hypergeometric distribution (20 points) (b) Use the general formulas and calculate the mean and standard deviation using the original equations; (10points) (c) By using the special formulas for the mean and the variance of a hypergeometric distribution (10points)
[25 points] Problem 4 - CDF Inversion Sampling ers coming from the U(0, 1) distribution into In notebook 12, we looked at one method many pieces of statistical software use to turn pseudorandom those with a normal distribution. In this problem we examine another such method. a) Simulating an Exponential i) The exponential distribution has pdf f(x) = le-ix for x > 0. Use the following markdown cell to compute by hand the cdf of the exponential. ii) The cdf...
3. Suppose that X has a Poisson distribution with mean μ=15. Use the 'cdf' command MTB > cdf; SUBC 〉 poisson 15. Find PX 〈 10)-[3] and P(15 X 20)= [3] 4. Suppose that Y has a hypergeometric distribution with parameters N = 20, M = 6, and n = 4, Use the command MTB > cdf 3; hypergeometric 20 6 4. a. [3] to find P(Y 53) = b. 3) Use the similar command to find P(Y > 2)...
3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist. & derive it. 4. X-i ~ cont with pdf fi(x) and CDF Fi(x), i=1, 2, , k. all independent. Define YjaFi(Xi), i=1, , k. Derive the distribution of
3. X is a continuous RV with pdf f(x) and CDF F(x). a) Derive the dist of Y=F(X) b) Show that Z=-21n(Y) has a Gamma dist....
1 Program 2-paramter Weibull distribution with β 100 rows by copying down the equation from Table 4.1. In the next column generate 1000 rows and in the next column 10 000 rows. Calculate the mean and standard deviation for each column. By hitting Recalculate' (typically F9) observe the mean and standard deviation values. What can you say about the variation for each group? 3.0 and η 000 into Excel spreadsheet and generate 2. When simulating the function Z-X where X...
Question 3 A more general form of Cauchy distribution is defined by the density function f(x; m, 7) = where m is the location parameter, is the scale parameter and they are both constants. We will create a function to simulate draws of a Cauchy(m, 7) distribution in this exercise using the inversion method. (a) (4 points) Derive the cdf, and the inverse function of cdf for Cauchy(m, n). Describe a procedure to generate independent observations from a Cauchy(m, 7)...
Problem 2. The annual maximum wind speed in a location in the United States has the Type II Largest Value distribution with mean 65 km/hr and standard deviation 20 km/hr. (a) Determine the parameters of the distribution and make a plot of the PDF. (b) What is the probability that the threshold of 100 km/hr will be exceeded in 10 years?
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