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1. Suppose you have a sample {x,...). If you...
Suppose you have a random sample {X1, X2, X3} of size n = 3. Consider the following three possible estimators for the p...
Suppose you have a random sample {X1, X2, X3} of size n = 3. Consider the following three possible estimators for the population mean u and variance o2 Дi 3D (X1+ X2+ X3)/3 Ti2X1/4 X2/2 X3/4 Дз — (Х+ X,+ X3)/4 (a) What is the bias associated with each estimator? (b) What is the variance associated with each estimator? (c) Does the fact that Var(i3) < Var(1) contradict the statement that X is the minimum variance unbiased estimator? Why or...
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. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and varia...
1. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and variance σχ2. Assume that n 2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes x] and x2. Let estimate f x of true mean ux be μΧ-(X1 + x2)/2. Then the random variable associated with estimate Axis estimator Ax- (XI...
Consider a random experiment that has as an outcome the number x. Let the associated variable be X, with true (population) and unknown probability density function fx(x), mean ux. and variance σχ2. A...
Consider a random experiment that has as an outcome the number x. Let the associated variable be X, with true (population) and unknown probability density function fx(x), mean ux. and variance σχ2. Assume that n-2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes xi and x2 Let estimate μ X of true mean #xbe μχ = (x1+x2)/2. Then the random variable associated with estimate μ xis estimator random 1. a. Show the...
The answer mean is 1/3, variance is 1/18 Problem 44.15 Suppose that X has a continuous...
The answer mean is 1/3, variance is 1/18
Problem 44.15 Suppose that X has a continuous distribution with pdf. fx (x) = 2x on (0,1) and 0 elsewhere. Suppose that Y is a continuous random variable such that the conditional distribution of Y given X- is uniform on the interval (0, x). Find the mean and variance of Y.
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with me...
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
v. suppose that X1,...,x, is a random sample with a common Nu d istribution. sample mean...
v. suppose that X1,...,x, is a random sample with a common Nu d istribution. sample mean X and sample variance SP are defined by X= 2 X, and S2 = 1 (x-7). Under our model, it can be shown that 8-N(, $?) and (n =]].S? - x- are independent random variables. Define the random variable T by We can express T as T = ola malga (n-1) Wi(n = 1) where Z = ~ N(0,1) and W ~ x-1 In...
The question is below. Please help me get through I really want to learn :( Thanks!...
The
question is below.
Please help me get through
I really want to learn :(
Thanks!
(2) (20 pts) Suppose we want to construct a continuous joint density function of the form fx.y(x,y) = c(x3 + 3x2y + 3xy® + y*), where c is some constant, and the variables X and Y are restricted to the real interval [0,1]. a) (2 pts) How can you tell, just by looking at this pdf, that Xand Y are dependent? b) (4 pts)...
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...
2. Suppose XX2,X is a random sample from an exponential distribution with . Let X(1) minX1,X2,...
2. Suppose XX2,X is a random sample from an exponential distribution with . Let X(1) minX1,X2, Xn), the minimum of the sample mean (a) Show that the estimator 6nx is an unbiased estimator of 8. (hint: you were asked to derive the distribution of X for a random sample from an exponential distribution on assignment 2 -you may use the result) (b) X, the sample mean, is also an unbiased estimator of . Which of the unbiased estimators, or X,...
Suppose you have a random sample {X1, X2, X3} of size n = 3. Consider the following three possible estimators for the population mean u and variance o2 Дi 3D (X1+ X2+ X3)/3 Ti2X1/4 X2/2 X3/4 Дз — (Х+ X,+ X3)/4 (a) What is the bias associated with each estimator? (b) What is the variance associated with each estimator? (c) Does the fact that Var(i3) < Var(1) contradict the statement that X is the minimum variance unbiased estimator? Why or...
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. Consider a random experiment that has as an outcome the number x. Let the associated random variable be X, with true (population) and unknown probability density function fx(x), mean ux, and variance σχ2. Assume that n 2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes x] and x2. Let estimate f x of true mean ux be μΧ-(X1 + x2)/2. Then the random variable associated with estimate Axis estimator Ax- (XI...
Consider a random experiment that has as an outcome the number x. Let the associated variable be X, with true (population) and unknown probability density function fx(x), mean ux. and variance σχ2. Assume that n-2 independent, repeated trials of the random experiment are performed, resulting in the 2-sample of numerical outcomes xi and x2 Let estimate μ X of true mean #xbe μχ = (x1+x2)/2. Then the random variable associated with estimate μ xis estimator random 1. a. Show the...
The answer mean is 1/3, variance is 1/18
Problem 44.15 Suppose that X has a continuous distribution with pdf. fx (x) = 2x on (0,1) and 0 elsewhere. Suppose that Y is a continuous random variable such that the conditional distribution of Y given X- is uniform on the interval (0, x). Find the mean and variance of Y.
I. Consider a variable y = θ + where θ is an unknown parameter and e is a random variable with mean zero. (a) What is the expected value of y? (b) Suppose you draw a sample of yi yn. Derive the least squares estimator for θ. For full credit you must check the 2nd order condition c) Can this estimator (0) be described as a method of moments estimator? (d) Now suppose є is independent normally distributed with mean...
v. suppose that X1,...,x, is a random sample with a common Nu d istribution. sample mean X and sample variance SP are defined by X= 2 X, and S2 = 1 (x-7). Under our model, it can be shown that 8-N(, $?) and (n =]].S? - x- are independent random variables. Define the random variable T by We can express T as T = ola malga (n-1) Wi(n = 1) where Z = ~ N(0,1) and W ~ x-1 In...
The
question is below.
Please help me get through
I really want to learn :(
Thanks!
(2) (20 pts) Suppose we want to construct a continuous joint density function of the form fx.y(x,y) = c(x3 + 3x2y + 3xy® + y*), where c is some constant, and the variables X and Y are restricted to the real interval [0,1]. a) (2 pts) How can you tell, just by looking at this pdf, that Xand Y are dependent? b) (4 pts)...
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...
2. Suppose XX2,X is a random sample from an exponential distribution with . Let X(1) minX1,X2, Xn), the minimum of the sample mean (a) Show that the estimator 6nx is an unbiased estimator of 8. (hint: you were asked to derive the distribution of X for a random sample from an exponential distribution on assignment 2 -you may use the result) (b) X, the sample mean, is also an unbiased estimator of . Which of the unbiased estimators, or X,...
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