Please help with the R code! Thanks!
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Please help with the R code! Thanks!
Assume that your data consists of x1, . ....
1. Let X1,... , Xn be IID random points from Exp(1/B). The PDF of Exp(1/B) is...
1. Let X1,... , Xn be IID random points from Exp(1/B). The PDF of Exp(1/B) is for x 〉 0. Let X,-1 Σー X, be the sample average. Let 3 be the parameter of interest that we want to estimate. Xi be the sample average. Let B be the parameter of (a) (1 pt) What is the bias and variance of using the sample average Xn as the estimator of 3? (b) (0.5 pt) What is the mean square error...
# 3. The following code draws a sample of size $n=30$ from a chi-square distribution with...
# 3. The following code draws a sample of size $n=30$ from a chi-square distribution with 15 degrees of freedom, and then puts $B=200$ bootstrap samples into a matrix M. After that, the 'apply' function is used to calculate the median of each bootstrap sample, giving a bootstrap sample of 200 medians. "{r} set.seed (117888) data=rchisq(30,15) M=matrix(rep(0,30*200), byrow=T, ncol=30) for (i in 1:200 M[i,]=sample(data, 30, replace=T) bootstrapmedians=apply(M,1,median) (3a) Use the 'var' command to calculate the variance of the bootstrapped medians....
Help me on Statistic Theory question please. assume that the random variables X1, · · ·...
Help me on Statistic Theory question please. assume that the random variables X1, · · · , Xn form a random sample of size n form the distribution specified in that exercise, and show that the statistic T specified in the exercise is a sufficient statistic for the parameter A normal distribution for which the mean µ is known and the variance σ 2 is unknown; T = Sigma i=1 to n (Xi − µ)^ 2 .
Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
1. Let X be an iid sample of size n from a continuous distribution with mean...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
1 Bookmark this page Setup: For all problems on this page, suppose you have data X],...,x...
1 Bookmark this page Setup: For all problems on this page, suppose you have data X],...,x . N (0,1) that is a random sample of identically and independently distributed standard normal random variables. Useful facts: The following facts might be useful: For a standard normal random variable X1, we have: E[X] =0, E[X{1=1, E(X) = 3. Sample mean 1.5 points possible (graded, results hidden) Consider the sample mean: X = x + X2+...+X,). What are the mean E [Xn] and...
Please Provide Code for above question , be sure that the C code compiles using GCC...
Please Provide Code for above question , be sure that the C code
compiles using GCC
Task 6: Arrays: Statistics Calculations Write a C program which accepts a "large" mumber of real numbers and calculates their sample mean and sample variance. Revision: From statistics, the sample variance, ,of N samples, X1, X2,..XN, can be calculated as: N mcan(X) ) 2. (Xt (1) N-1 There are many algorithms for calculating a data set's variance. For this task you should implement the...
SOLVE the following in R code: iid Let X1, , Xn ~ U (0,0). We are...
SOLVE the following in R code:
iid Let X1, , Xn ~ U (0,0). We are going to compare two estimators for θ: 01-2X, the method of moments estimator -maxX.... X1, the maximum likelihood estimator I. Generate 50,000 samples of size n-50 from U(0,5). For each sample compute both θ1 and 02 (Hint: You can use the R cornmand max (v) to find the maximum entry of a vector v). The results should be collected in two vectors of length...
Problem 4 Define f(x) as follows θ2 -1<=x<0 1-θ2 0<=x>1 0 otherwise Let X1, … Xn be iid random variables with density f for some unknown θ...
Problem 4 Define f(x) as follows θ2 -1<=x<0 1-θ2 0<=x>1 0 otherwise Let X1, … Xn be iid random variables with density f for some unknown θ (0,1), Let a be the number of Xi which are negatives and b be the number of Xi which are positive. Total number of samples n = a+b. Find he Maximum likelihood estimator of θ? Is it asymptotically normal in this sample? Find the asymptotic variance Consider the following hypotheses: H0: X is...
Independent random samples X1, X2, . . . , Xn are from exponential distribution with pdfs...
Independent random samples X1, X2, . . . , Xn are from
exponential distribution with pdfs
, xi > 0, where λ is fixed but unknown. Let
. Here we have a relative large sample size n = 100.
(ii) Notice that the population mean here is µ = E(X1) = 1/λ ,
population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the
sample standard deviation s = 10, sample average
= 5, construct a 95% large-sample approximate confidence...
1. Let X1,... , Xn be IID random points from Exp(1/B). The PDF of Exp(1/B) is for x 〉 0. Let X,-1 Σー X, be the sample average. Let 3 be the parameter of interest that we want to estimate. Xi be the sample average. Let B be the parameter of (a) (1 pt) What is the bias and variance of using the sample average Xn as the estimator of 3? (b) (0.5 pt) What is the mean square error...
# 3. The following code draws a sample of size $n=30$ from a chi-square distribution with 15 degrees of freedom, and then puts $B=200$ bootstrap samples into a matrix M. After that, the 'apply' function is used to calculate the median of each bootstrap sample, giving a bootstrap sample of 200 medians. "{r} set.seed (117888) data=rchisq(30,15) M=matrix(rep(0,30*200), byrow=T, ncol=30) for (i in 1:200 M[i,]=sample(data, 30, replace=T) bootstrapmedians=apply(M,1,median) (3a) Use the 'var' command to calculate the variance of the bootstrapped medians....
Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
1. Let X be an iid sample of size n from a continuous distribution with mean /i, variance a2 and such that Xi e [0, 1] for all i e {1,...,n}. Let X = average. For a E (0,1), we wish to obtain a number q > 0 such that: (1/n) Xi be the sample Р(X € |и — 9. и + q) predict with probability approximately In other words, we wish to sample of size n, the average X...
1 Bookmark this page Setup: For all problems on this page, suppose you have data X],...,x . N (0,1) that is a random sample of identically and independently distributed standard normal random variables. Useful facts: The following facts might be useful: For a standard normal random variable X1, we have: E[X] =0, E[X{1=1, E(X) = 3. Sample mean 1.5 points possible (graded, results hidden) Consider the sample mean: X = x + X2+...+X,). What are the mean E [Xn] and...
Please Provide Code for above question , be sure that the C code
compiles using GCC
Task 6: Arrays: Statistics Calculations Write a C program which accepts a "large" mumber of real numbers and calculates their sample mean and sample variance. Revision: From statistics, the sample variance, ,of N samples, X1, X2,..XN, can be calculated as: N mcan(X) ) 2. (Xt (1) N-1 There are many algorithms for calculating a data set's variance. For this task you should implement the...
SOLVE the following in R code:
iid Let X1, , Xn ~ U (0,0). We are going to compare two estimators for θ: 01-2X, the method of moments estimator -maxX.... X1, the maximum likelihood estimator I. Generate 50,000 samples of size n-50 from U(0,5). For each sample compute both θ1 and 02 (Hint: You can use the R cornmand max (v) to find the maximum entry of a vector v). The results should be collected in two vectors of length...
Independent random samples X1, X2, . . . , Xn are from
exponential distribution with pdfs
, xi > 0, where λ is fixed but unknown. Let
. Here we have a relative large sample size n = 100.
(ii) Notice that the population mean here is µ = E(X1) = 1/λ ,
population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the
sample standard deviation s = 10, sample average
= 5, construct a 95% large-sample approximate confidence...
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