Please give detailed steps of part a. Thank you.
![4. Recall that the method of moments estimator of the population variance a2-EX-E(X)]2 is given by V12 X, - X)2. . Explain intutitvely why ơMOM defined above is the MOM estimator for σ2 b. Use the represenation from part 3. to show that ơMOM is a consistent estimator of σ2](http://img.homeworklib.com/questions/85014620-78c7-11ea-a9f3-3bc604812178.png?x-oss-process=image/resize,w_560)
Homework Answers
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Please give detailed steps of part a. Thank you.
4. Recall that the method of moments...
Please give detailed steps. Thank you. 5. Let {X, : i-1..n^ denote a random sample of...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
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)...
MoM stands for Method of Moments. 4. (a) If X Geometric(p), prove that the moment-generating function...
MoM stands for Method of Moments.
4. (a) If X Geometric(p), prove that the moment-generating function for X is Mx(t) pe 1-(1-p)e' (b) Use your result of part (a) to show that E(X) = p and V(X) = Now, we have X1, X2,... X, d Geometricíp). (c) Find a MoM estimator for p based on the first moment. (d) Explain why your estimator makes sense intuitively. (e) Use the following data to give a point estimate of p: XnGeometric(p 3,...
Could you please give detailed steps? Thanks! Consider a random sample from the Poisson(0) distribution (e.g....
Could you please give detailed
steps? Thanks!
Consider a random sample from the Poisson(0) distribution (e.g. this setup could apply to the number of arrests example from class) You may take it as given that if X ~Poisson(0) then E[X_ θ)41-30" +θ (rememeber this is this is the 4th central moment or one of the definitions of kuutosis 3- (this is another commonly used definition of the kurtosis) (no need to show any of these) a. You wish to estimate...
Please give a detailed explain of integration by parts and the induction to prove the equation....
Please give a detailed explain of integration by parts and the
induction to prove the equation. Thank you!
Let Z1, Z2.. be a sequence of IID random variables with mean 0 and variance 1 and define i=1 and Another method of proof of CLT (the method of "moments") works by showing that for each m, the limit Lm exists, and the sequence satisfies the recurrence relation Use integration by parts to show that the sequence Rm variable, satisfies the same...
Can someone please give a detailed explanation of the steps within this reaction? Thank you. ...
Can someone please give a detailed
explanation of the steps within this reaction? Thank you.
Give the products of the reaction below. Give the structure of all possible products and give the names for each product. b) Elimination of water from 2-butanol
Please give detailed steps. Thank you. 2. Consider the following joint distribution of two discrete variables...
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
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...
Please give detailed steps. Thank you. 2.1 Representing a preference Consider my preference over bundles (x1,x2),...
Please give detailed steps. Thank you.
2.1 Representing a preference Consider my preference over bundles (x1,x2), where x0 andx20. You do not know all of nt pairwise comparisons in my preference, but you do know the following: Suppose you also know that my preference is rational, strictly monotonic, and strictly convex Can you infer how my preference compares the following pairs? Explain each one briefly. a) (3,7) versus (1,7), b) (3,7) versus (7,5), c) (1,7) versus (4,6), d) (7,5) versus...
Please solve each part of the question with clear and detailed reasoning. Thank you in advance....
Please solve each part of the question with clear and detailed
reasoning. Thank you in advance.
EXERCISE 1 The robust estimator of of the variogram (Cressie and Hawkins (1980)) given by 1 4 I ( z(s +h)-2(8) N(h) N(h) 27(h) uses the transformatiorn 0.457 + N (h) 0.494 Consider now the class of power transformations 2 2y(h) a. Find the mean and variance of a X21 λ , where λ-, 1, b. Let X ~ χ . Find and plot...
Please give detailed steps. Thank you.
5. Let {X, : i-1..n^ denote a random sample of size n from a population described by a random varaible X following a Poisson(θ) distribution with PDF given by θ and var(X) θ (i.e. you do not You may take it as given that E(X) need to show these) a. Recall that an estimator is efficient, if it satisfies 2 conditions: 2) it achieves the Cramer-Rao Lower Bound (CLRB) for unbiased estimators: Show that...
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)...
MoM stands for Method of Moments.
4. (a) If X Geometric(p), prove that the moment-generating function for X is Mx(t) pe 1-(1-p)e' (b) Use your result of part (a) to show that E(X) = p and V(X) = Now, we have X1, X2,... X, d Geometricíp). (c) Find a MoM estimator for p based on the first moment. (d) Explain why your estimator makes sense intuitively. (e) Use the following data to give a point estimate of p: XnGeometric(p 3,...
Could you please give detailed
steps? Thanks!
Consider a random sample from the Poisson(0) distribution (e.g. this setup could apply to the number of arrests example from class) You may take it as given that if X ~Poisson(0) then E[X_ θ)41-30" +θ (rememeber this is this is the 4th central moment or one of the definitions of kuutosis 3- (this is another commonly used definition of the kurtosis) (no need to show any of these) a. You wish to estimate...
Please give a detailed explain of integration by parts and the
induction to prove the equation. Thank you!
Let Z1, Z2.. be a sequence of IID random variables with mean 0 and variance 1 and define i=1 and Another method of proof of CLT (the method of "moments") works by showing that for each m, the limit Lm exists, and the sequence satisfies the recurrence relation Use integration by parts to show that the sequence Rm variable, satisfies the same...
Can someone please give a detailed
explanation of the steps within this reaction? Thank you.
Give the products of the reaction below. Give the structure of all possible products and give the names for each product. b) Elimination of water from 2-butanol
Please give detailed steps. Thank you.
2. Consider the following joint distribution of two discrete variables X and Y: fx,y(x, y) 01 2 3 お88 Recall that the marginal distribution of X is defined as: fx(x) and the marginal distribution of Y is defined as fy(v) -xf(i) Find fx(x) and fy(y) in the support of X and Y (or in simpler terms, find 1), P(Y = 0), P(Y-1), P(Y-2) and P(Y P(X-0), P(X 3)) b. The conditional density of Y...
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...
Please give detailed steps. Thank you.
2.1 Representing a preference Consider my preference over bundles (x1,x2), where x0 andx20. You do not know all of nt pairwise comparisons in my preference, but you do know the following: Suppose you also know that my preference is rational, strictly monotonic, and strictly convex Can you infer how my preference compares the following pairs? Explain each one briefly. a) (3,7) versus (1,7), b) (3,7) versus (7,5), c) (1,7) versus (4,6), d) (7,5) versus...
Please solve each part of the question with clear and detailed
reasoning. Thank you in advance.
EXERCISE 1 The robust estimator of of the variogram (Cressie and Hawkins (1980)) given by 1 4 I ( z(s +h)-2(8) N(h) N(h) 27(h) uses the transformatiorn 0.457 + N (h) 0.494 Consider now the class of power transformations 2 2y(h) a. Find the mean and variance of a X21 λ , where λ-, 1, b. Let X ~ χ . Find and plot...
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