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TOPIC:Method of moment estimator.
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5.2.1. Let XX be a random sample of size n from the geometric distribution for which...
LetX1,...,Xn be a random sample of size n from the geometric distribution for which p is...
LetX1,...,Xn be a random sample of size n from the geometric distribution for which p is the probability of success. (a) Use the method of moments to find a point estimator for p. (b) Use the following data (simulated from geometric distribution) to find the moment estimator for p: 2 5 7 43 18 19 16 11 22 4 34 19 21 23 6 21 7 12 The pdf of a geometric distribution is f(x)= p(1-p)^x-1, for x,.... Also population...
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution...
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution for which p is the probability of success. We know the maximum likelihood estimator for p is p = 1 Σ_i Xi. ·Show that p is an unbiased estimator of p.
Number 2 only PLEASE 1. [40] 6.4-5. Let Xi, X2..,Xn be a random sample from dis-...
Number 2 only PLEASE
1. [40] 6.4-5. Let Xi, X2..,Xn be a random sample from dis- tributions with the given probability density functions. In each case, find the maximum likelihood estimator . 6.4-10. Let X1, X2,... ,Xn be a random sample of size n from a geometric distribution for which p is the probabil- ity of success. (a) Use the method of moments to find a point estimate 2. [20] for p. 100] 6.5-3. The midterm and final exam scores...
Question 3 [25] , Yn denote a random sample of size n from a Let Y,...
Question 3 [25] , Yn denote a random sample of size n from a Let Y, Y2, population with an exponential distribution whose density is given by y > 0 if o, otherwise -E70 cumulative distribution function f(y) L ..,Y} denotes the smallest order statistics, show that Y1) = min{Y1, =nYa) 3.1 show that = nY1) is an unbiased estimator for 0. /12/ /13/ 3.2 find the mean square error for MSE(e). 2 f-llays Iat-k)-at 1-P Question 4[25] 4.1 Distinguish...
Let X1, X2, ..., Xn be a random sample of size n from the distribution with...
Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function f(x1) = 2 Æ e-dz?, x > 0, 1 > 0. a. Obtain the maximum likelihood estimator of 1 . Enter a formula below. Use * for multiplication, / for divison, ^ for power. Use m1 for the sample mean X, m2 for the second moment and pi for the constant n. That is, m1 = * = *Šxi, m2 =...
Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x;...
Let X1, ..., X50 denote a random sample of size 50 from the geometric distribution f(x; θ) = θ(1 − θ) x−1 for x = 1, 2, ... and 0 < θ < 1. Suppose that after taking the observations we find that ¯x = 5. 8. a) Find the maximum likelihood estimator ˆθ of θ. b) Find E[X¯] and var(X¯). c) Use part (b) above together with the CLT and delta method to find the limiting distribution of √...
Problem5 Let x, ,x, be a random sample from normal population Na, σ Find method of moments estima...
Problem5 Let x, ,x, be a random sample from normal population Na, σ Find method of moments estimator of σ: is it unbiased? Problem6 Random variable X has density f(x)-ax+ Bx' in the interval (0.1) and 0 elsewhere. Given that EX (a) find α, β, () find P Xx-o.s 0.09 (6) Let you have sample of size 25, with sample mean R.Estimate the probability R>0.8).Formulate the assumptions
Problem5 Let x, ,x, be a random sample from normal population Na, σ...
Let X1, X2,.. .Xn be a random sample of size n from a distribution with probability...
Let X1, X2,.. .Xn be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of θ, θ. Use this maximum likelihood estimator to obtain an estimate of P[X > 4 when 0.50, 2 1.50, x 4.00, 4 3.00.
QUESTION 5 Let Y , Y2, , Yn denote a random sample of size n from...
QUESTION 5 Let Y , Y2, , Yn denote a random sample of size n from a population whose density is given by (a) Find the method of moments estimator for β given that α is known. Find the mean and variance of p (b) (c) show that β is a consistent estimator for β.
Let X1, X2,... X,n be a random sample of size n from a distribution with probability...
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
1. Let X1, X2,... .Xn be a random sample of size n from a Bernoulli distribution for which p is the probability of success. We know the maximum likelihood estimator for p is p = 1 Σ_i Xi. ·Show that p is an unbiased estimator of p.
Number 2 only PLEASE
1. [40] 6.4-5. Let Xi, X2..,Xn be a random sample from dis- tributions with the given probability density functions. In each case, find the maximum likelihood estimator . 6.4-10. Let X1, X2,... ,Xn be a random sample of size n from a geometric distribution for which p is the probabil- ity of success. (a) Use the method of moments to find a point estimate 2. [20] for p. 100] 6.5-3. The midterm and final exam scores...
Question 3 [25] , Yn denote a random sample of size n from a Let Y, Y2, population with an exponential distribution whose density is given by y > 0 if o, otherwise -E70 cumulative distribution function f(y) L ..,Y} denotes the smallest order statistics, show that Y1) = min{Y1, =nYa) 3.1 show that = nY1) is an unbiased estimator for 0. /12/ /13/ 3.2 find the mean square error for MSE(e). 2 f-llays Iat-k)-at 1-P Question 4[25] 4.1 Distinguish...
Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function f(x1) = 2 Æ e-dz?, x > 0, 1 > 0. a. Obtain the maximum likelihood estimator of 1 . Enter a formula below. Use * for multiplication, / for divison, ^ for power. Use m1 for the sample mean X, m2 for the second moment and pi for the constant n. That is, m1 = * = *Šxi, m2 =...
Problem5 Let x, ,x, be a random sample from normal population Na, σ Find method of moments estimator of σ: is it unbiased? Problem6 Random variable X has density f(x)-ax+ Bx' in the interval (0.1) and 0 elsewhere. Given that EX (a) find α, β, () find P Xx-o.s 0.09 (6) Let you have sample of size 25, with sample mean R.Estimate the probability R>0.8).Formulate the assumptions
Problem5 Let x, ,x, be a random sample from normal population Na, σ...
Let X1, X2,.. .Xn be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of θ, θ. Use this maximum likelihood estimator to obtain an estimate of P[X > 4 when 0.50, 2 1.50, x 4.00, 4 3.00.
QUESTION 5 Let Y , Y2, , Yn denote a random sample of size n from a population whose density is given by (a) Find the method of moments estimator for β given that α is known. Find the mean and variance of p (b) (c) show that β is a consistent estimator for β.
Let X1, X2,... X,n be a random sample of size n from a distribution with probability density function obtain the maximum likelihood estimator of λ, λ. Calculate an estimate using this maximum likelihood estimator when 1 0.10, r2 0.20, 0.30, x 0.70.
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