Is it better to use Metropolis algorithm rather than Accept-Reject algorithm in generating a random sample...
Is it better to use Metropolis algorithm rather than Accept-Reject algorithm in generating a random sample with Student's t distribution?
Homework Answers
- If we use one dimensional student t distribution , then the answer is No. We don't use Metropolis algorithm in one dimensional distribution, since Metropolis algorithm has autocorrelation problem. This problem can avoided in one dimensional distribution by using Accept Rejection algorithm..
- But if we have a multidimensional student t distribution then we use Metropolis algorithm to generate a random sample.
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Is it better to use Metropolis algorithm rather than
Accept-Reject algorithm in generating a random sample...
For v=2, 10 and 25, generate a sample size of 100 using Metropolis Algorithm and Accept/Reject Al...
For v=2, 10 and 25, generate a sample size of 100 using Metropolis Algorithm and Accept/Reject Algorithm. Which is preferrable?
5. For α > 0 and β > 0, consider the following accept-reject algorithm: (1) Generate...
5. For α > 0 and β > 0, consider the following accept-reject algorithm: (1) Generate Ul and U2 iid uniform (0. 1) random variables. Set Vi-Ulla and U11/g ; else go to step l (3) Deliver X. Show that X has a beta distribution with parameter α and β.
How can the use of a restricted rather than a random sample affect the results of an analysis?
How can the use of a restricted rather than a random sample affect the results of an analysis?
9. (9 pts) The random variable ??~??????????(∝= 2, ?? = 4). Use the method of moment-generating...
9. (9 pts) The random variable ??~??????????(∝= 2, ?? = 4). Use
the method of moment-generating functions to prove that the moment
generating function for the random variable ?? = 3?? + 5 is
10.
9. (9 pts) The random variable Y-Gamma(α-2. functions to prove that the moment generating function for the random variable W mw(t)120)2 4). Use the method of moment-generating 3Y 5 is est (1-12t)2 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 15 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 14.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown.No, the x distribution is skewed left. No, the x distribution...
For a random sample of 36 data pairs, the sample mean of the differences was 0.72....
For a random sample of 36 data pairs, the sample mean of the differences was 0.72. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. No, the sample size is not larger than 30. Yes, the sample size is larger than 30. No, the...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample...
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 9 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 8.5. (a) Is it appropriate to use a Student's t distribution? Explain. Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. No, the x distribution is skewed left. No, the...
Use the given moment-generating function, Mx(t), to identify the distribution of the random variable, X in...
Use the given moment-generating function, Mx(t), to identify the distribution of the random variable, X in each of the following cases. (Specify the exact type of distribution and the value(s) of any relevant parameters(s): 1. (a) M(-3 (b) M() exp(2e -2) Ce) M T112t)3 (f) Mx(t) = ( 1-3t 10 ) (d) Mx(t)= exp(2t2_t) (e) Mx(t)= - m01 -2t)!
Would you favor spending more federal tax money on the arts? Of a random sample of...
Would you favor spending more federal tax money on the arts? Of a random sample of n = 93 politically conservative voters, 1 = 17 responded yes. Another random sample of n2 = 78 politically moderate voters showed that r2 - 22 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use a = 0.05....
Consider a MergeSort-like algorithm in which the array is split into thirds, rather than halves. (a)...
Consider a MergeSort-like algorithm in which the array is split into thirds, rather than halves. (a) Write pseudo-code for your algorithm. You may assume a three-way merge algorithm is available. Your algorithm should work for general n, i.e., even if the size of the array is not a power of 3. (b) Use the tree method to analyze exactly how many comparisons your algorithm uses. You may assume that the size of the array is a power of 3. Assume...
5. For α > 0 and β > 0, consider the following accept-reject algorithm: (1) Generate Ul and U2 iid uniform (0. 1) random variables. Set Vi-Ulla and U11/g ; else go to step l (3) Deliver X. Show that X has a beta distribution with parameter α and β.
How can the use of a restricted rather than a random sample affect the results of an analysis?
9. (9 pts) The random variable ??~??????????(∝= 2, ?? = 4). Use
the method of moment-generating functions to prove that the moment
generating function for the random variable ?? = 3?? + 5 is
10.
9. (9 pts) The random variable Y-Gamma(α-2. functions to prove that the moment generating function for the random variable W mw(t)120)2 4). Use the method of moment-generating 3Y 5 is est (1-12t)2 10, (9 pts) Suppose that Y has a gamma distribution with α-n/2 for...
For a random sample of 36 data pairs, the sample mean of the differences was 0.72. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. No, the sample size is not larger than 30. Yes, the sample size is larger than 30. No, the...
Use the given moment-generating function, Mx(t), to identify the distribution of the random variable, X in each of the following cases. (Specify the exact type of distribution and the value(s) of any relevant parameters(s): 1. (a) M(-3 (b) M() exp(2e -2) Ce) M T112t)3 (f) Mx(t) = ( 1-3t 10 ) (d) Mx(t)= exp(2t2_t) (e) Mx(t)= - m01 -2t)!
Would you favor spending more federal tax money on the arts? Of a random sample of n = 93 politically conservative voters, 1 = 17 responded yes. Another random sample of n2 = 78 politically moderate voters showed that r2 - 22 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use a = 0.05....
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