Using a bar length μ
| Using a bar of length μ, you are going to lay out a square plot in which the length of each side will be length μ. Thus the area of the plot will be μ2. However, you do not know the value of μ and so you decide to make 15 independent measurements of the bar, {Xi : i = 1, … , n}. Assume that each Xi has mean μ (unbiased measurement) and variance σ2 = 0.4. |
| (a) | Find the bias of the random variable X_2 as an estimator for μ2. |
| (b) | For what value of k is the estimator X_2 − kS2 unbiased for μ2? |
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Using a long rod that has length μ you are going to lay out a square...
Using a long rod that has length μ you are going to lay out a square plot in which the length of each side is Thus the area of the plot will be However, you do not know the value of μ, so you decide to make n independent measurements X1,X2, ,X, of the length. Assume that each Xi has mean μ and variance σ Show that X 2 is not an unbiased estimator for μ2 What is the bias?...
Using a long rod that has length , you are going to lay out a square...
Using a long rod that has length , you are going to lay out a
square plot in which the length of each 2. side is . Thus the area
of the plot will be However, you do not know the value of , so you
decide to make n independent measurements X1;X2; :::;Xn of the
length. Assume that each Xi has mean 2. (unbiased measurements) and
variance o^2.
Question C only, Now if I estimate u using both X1...
3. Using a long rod that has length p, you are going to lay out a...
3. Using a long rod that has length p, you are going to lay out a square plot in which the length of each side is u. Thus the area of the plot will be u?. However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X; has mean u (unbiased measurements) and variance o2. a) Is X2 unbiased for u? ? why...
Now if I estimate y using both Xi and X, which estimator is better in terms...
Now if I estimate y using both Xi and X, which estimator is better in terms of efficiency? (3] 3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be u2. However, you do not know the value of , so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume...
3. Using a long rod that has length y, you are going to lay out a...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be ?. However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X, has mean y (unbiased measurements) and variance o?. a) Is X2 unbiased for ? why or...
3. Using a long rod that has length y, you are going to lay out a...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is u. Thus the area of the plot will be ? However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., X., of the length. Assume that each X; has mean 4 (unbiased measurements) and variance o? a) Is X2 unbiased for u?? why or...
3. Using a long rod that has length y, you are going to lay out a...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be j?. However, you do not know the value of u, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X; has mean u (unbiased measurements) and variance o?. a) Is Xunbiased for u? ? why or...
can anyone help me with #3, especially c) thank you 3. Using a long rod that...
can anyone help me with #3, especially c) thank you
3. Using a long rod that has length, you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be. However, you do not know the value of , so you decide to make n independent measurements X1, X2, ..., X, of the length. Assume that each Xhas mean (unbiased measurements) and variance o?. a) Is...
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...
4. Xi ,i = 1, , n are iid N(μ, σ2). (a) Find the MLE of...
4. Xi ,i = 1, , n are iid N(μ, σ2). (a) Find the MLE of μ, σ2. Are these unbiased estimators of μ and of σ2 respectively? Aside: You can use your result in (b) to justify your answer for the bias part of the MLE estimator of σ2 (b) In this part you will show, despite that the sample variance is an unbiased estimator of σ2, that the sample standard deviation is is a biased estimator of σ....
Using a long rod that has length μ you are going to lay out a square plot in which the length of each side is Thus the area of the plot will be However, you do not know the value of μ, so you decide to make n independent measurements X1,X2, ,X, of the length. Assume that each Xi has mean μ and variance σ Show that X 2 is not an unbiased estimator for μ2 What is the bias?...
Using a long rod that has length , you are going to lay out a
square plot in which the length of each 2. side is . Thus the area
of the plot will be However, you do not know the value of , so you
decide to make n independent measurements X1;X2; :::;Xn of the
length. Assume that each Xi has mean 2. (unbiased measurements) and
variance o^2.
Question C only, Now if I estimate u using both X1...
3. Using a long rod that has length p, you are going to lay out a square plot in which the length of each side is u. Thus the area of the plot will be u?. However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X; has mean u (unbiased measurements) and variance o2. a) Is X2 unbiased for u? ? why...
Now if I estimate y using both Xi and X, which estimator is better in terms of efficiency? (3] 3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be u2. However, you do not know the value of , so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be ?. However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X, has mean y (unbiased measurements) and variance o?. a) Is X2 unbiased for ? why or...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is u. Thus the area of the plot will be ? However, you do not know the value of p, so you decide to make n independent measurements X1, X2, ..., X., of the length. Assume that each X; has mean 4 (unbiased measurements) and variance o? a) Is X2 unbiased for u?? why or...
3. Using a long rod that has length y, you are going to lay out a square plot in which the length of each side is p. Thus the area of the plot will be j?. However, you do not know the value of u, so you decide to make n independent measurements X1, X2, ..., Xn of the length. Assume that each X; has mean u (unbiased measurements) and variance o?. a) Is Xunbiased for u? ? why or...
can anyone help me with #3, especially c) thank you
3. Using a long rod that has length, you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be. However, you do not know the value of , so you decide to make n independent measurements X1, X2, ..., X, of the length. Assume that each Xhas mean (unbiased measurements) and variance o?. a) Is...
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...
4. Xi ,i = 1, , n are iid N(μ, σ2). (a) Find the MLE of μ, σ2. Are these unbiased estimators of μ and of σ2 respectively? Aside: You can use your result in (b) to justify your answer for the bias part of the MLE estimator of σ2 (b) In this part you will show, despite that the sample variance is an unbiased estimator of σ2, that the sample standard deviation is is a biased estimator of σ....
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