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Suppose population 1 has mean with variance σ2 and population 2 has mean μ2 with the...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2...
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with...
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
x, and S1 are the sample mean and sample variance from a population with mean μ|...
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 a...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased estimator for the common standard deviation of two independent sam ples Let Yi, Yi2, ..., Yini denote the random sample of size n from the first population with population mean μ| and population variance σ, and let Y21, Y22, ..., Y2na denote an independent random sample of size n2 from the second population with population mean μ2 and population mean ơ3. Sup- pose that...
5. Let 11,D, , , ,Zn and yı, y2, . . . , ym denote independent...
5. Let 11,D, , , ,Zn and yı, y2, . . . , ym denote independent observed random samples of size n and m taken from two normally distributed populations with the same mean μ but different variances σ and σ . lihood estimator for the common mean μ based on the combined sample Find the maximum like . Is pmle unbiased? Find the variance of nle. - Define the following estimator n+ m Is μ unbiased. Find the variance...
Having the worst time trying to answer these three questions below. Assume that σ21=σ22=σ2. Calculate the...
Having the worst time trying to answer these three questions below. Assume that σ21=σ22=σ2. Calculate the pooled estimator of σ2 when the first sample gives s21=128 and the second independent sample gives s22= 128, and n1=n2=36. Give your answer to two decimal places , do not round up or down. And .. Two independent random samples have been slected ; 111 observations from population one and 143 observations from population two. From previous experience it is known that the standard...
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2,...
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2, for this random sample. (b) Derive the maximum likelihood estimator (MLE) of μ and σ2 denoted μ and σ2, respectively. (c) Find the MLE of μ3 (d) Derive the method of moment estimator of μ and σ2, denoted μΜΟΜΕ and σ2MOME, respectively (e) Show that μ and...
please answer the questions easily Suppose X1, X2, X3 is a random sample from a normal...
please answer the questions easily
Suppose X1, X2, X3 is a random sample from a normal population with mean μ and variance (a) I,'ind i.he variallex, of Y , x..:.: Xy/X.t as an ( tinai." r of μ (b) Find the variance of Z-A+x2+x3 as an estimator of μ. (c) Which estimator is more efficient (i.e. has the smallest variance)? Consider a random sample of size n from a normal population with known mean μ and unknown variance σ2. Let...
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2
Suppose population l has mean ,11 with variance σ2 and population 2 has mean Ha with the same variance σ2. Let s' and s denote the sample variances from two samples with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator (m-1)sit (n2-1)d ni t n22 pooled is an unbiased estimator of σ2
x, and S1 are the sample mean and sample variance from a population with mean μ| and variance ơf. Similarly, X2 and S1 are the sample mean and sample variance from a second population with mean μ and variance σ2. Assume that these two populations are independent, and the sample sizes from each population are n,and n2, respectively. (a) Show that X1-X2 is an unbiased estimator of μ1-μ2. (b) Find the standard error of X, -X. How could you estimate...
3. You have two independent random samples: XiXX from a population with mean In and variance σ2 and Y, Y2, , , , , Y,n from a population with mean μ2 and variance σ2. Note that the two populations share a common variance. The two sample variances are Si for the first sample and Si for the second. We know that each of these is an unbiased estimator of the common population variance σ2, we also know that both of...
I1. Follow the steps below to show that the pooled estimator $p is an unbi- ased estimator for the common standard deviation of two independent sam ples Let Yi, Yi2, ..., Yini denote the random sample of size n from the first population with population mean μ| and population variance σ, and let Y21, Y22, ..., Y2na denote an independent random sample of size n2 from the second population with population mean μ2 and population mean ơ3. Sup- pose that...
5. Let 11,D, , , ,Zn and yı, y2, . . . , ym denote independent observed random samples of size n and m taken from two normally distributed populations with the same mean μ but different variances σ and σ . lihood estimator for the common mean μ based on the combined sample Find the maximum like . Is pmle unbiased? Find the variance of nle. - Define the following estimator n+ m Is μ unbiased. Find the variance...
1. (40) Suppose that X1, X2, Xn forms an independent and identically distributed sample from a normal distribution with mean μ and variance σ2, both unknown: 2nơ2 (a) Derive the sample variance, S2, for this random sample. (b) Derive the maximum likelihood estimator (MLE) of μ and σ2 denoted μ and σ2, respectively. (c) Find the MLE of μ3 (d) Derive the method of moment estimator of μ and σ2, denoted μΜΟΜΕ and σ2MOME, respectively (e) Show that μ and...
please answer the questions easily
Suppose X1, X2, X3 is a random sample from a normal population with mean μ and variance (a) I,'ind i.he variallex, of Y , x..:.: Xy/X.t as an ( tinai." r of μ (b) Find the variance of Z-A+x2+x3 as an estimator of μ. (c) Which estimator is more efficient (i.e. has the smallest variance)? Consider a random sample of size n from a normal population with known mean μ and unknown variance σ2. Let...
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