4. Let Xi, . . . , xn be a random sample from the inverse Gaussian...

Question

Question

4. Let Xi, . . . , xn be a random sample from the inverse Gaussian distribution, IG(μ, λ), whose pdf is: (a) Show that the MLE of μ and λ are μ-X and (b) It is known that n)/λ ~X2-1. Use this to derive a 100 . (1-a)% CI for λ.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Gluen thot 9 du 从 u s 씨 . 9 9刁 X92- よこ49

Add a comment

Answer 2

Similar Homework Help Questions

4. Let Xi, . . . , xn be a random sample from the inverse Gaussian...

4. Let Xi, . . . , xn be a random sample from the inverse Gaussian distribution, IG(μ, λ), whose pdf is: (a) Show that the MLE of μ and λ are μ-X and (b) It is known that n)/λ ~X2-1. Use this to derive a 100 . (1-a)% CI for λ.
NOTE: DO PART c) ONLY PLEASE INCLUDE THE R CODES ALONG WITH THE PLOTS 4. Let...

NOTE: DO PART c) ONLY PLEASE INCLUDE THE R CODES ALONG WITH THE PLOTS 4. Let XI, . .. , Xn be a random sample from the inverse Gaussian distribution. IG(μ, λ), whose pdf is (a) Show that the MLE of μ and λ are μ-X and (b) It is known that nA/λ ~ χ2-1. Use this to derive a 100-(1-a)% CI for λ (c) (R) Consider the following dataset 10.6, 91.3, 51.7, 2.2, 3.8, 6.0, 17.8, 131.8, 31.0, 4.2,...
NOTE: DO PART c) ONLY PLEASE INCLUDE THE R CODES ALONG WITH THE PLOTS 4. Let...

NOTE: DO PART c) ONLY PLEASE INCLUDE THE R CODES ALONG WITH THE PLOTS 4. Let XI, . .. , Xn be a random sample from the inverse Gaussian distribution. IG(μ, λ), whose pdf is (a) Show that the MLE of μ and λ are μ-X and (b) It is known that nA/λ ~ χ2-1. Use this to derive a 100-(1-a)% CI for λ (c) (R) Consider the following dataset 10.6, 91.3, 51.7, 2.2, 3.8, 6.0, 17.8, 131.8, 31.0, 4.2,...

Let Xi,...,Xn be a random sample from a two parameter exponential distribution with pa- rameter θ...

Let Xi,...,Xn be a random sample from a two parameter exponential distribution with pa- rameter θ (λ, μ), (a) Show that the distribution of Ti = log(X(n)-X) +log λ is free of θ. Îs an ancillary statistics (b) show that 72- Xu is ancillary X-X Let Xi,...,Xn be a random sample from a two parameter exponential distribution with pa- rameter θ (λ, μ), (a) Show that the distribution of Ti = log(X(n)-X) +log λ is free of θ. Îs an...
1. Let Xi, X2,.., Xn be a random sample drawn from some population with mean μ--2λ and variance σ...

1. Let Xi, X2,.., Xn be a random sample drawn from some population with mean μ--2λ and variance σ2-4, where λ is a parameter. Define 2n We use V, to estimate λ. (a) Show that is an unbiased estimator for λ. (b) Let ơin be the variance of V,, . Show that lin ơi,- 1. Let Xi, X2,.., Xn be a random sample drawn from some population with mean μ--2λ and variance σ2-4, where λ is a parameter. Define 2n...
2. Let Xi, X2, . Xn be a random sample from a distribution with the probability...

2. Let Xi, X2, . Xn be a random sample from a distribution with the probability density function f(x; θ-829-1, 0 < x < 1,0 < θ < oo. Find the MLE θ

Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n)...

Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n). Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n).
4. Let Xi, X2, ensity function f(r; , Xn be a random sample from a distribution...

4. Let Xi, X2, ensity function f(r; , Xn be a random sample from a distribution with the probability θ)-(1/2)e-11-01,-oo <エく00,-00 < θ < oo. Find the d MLE θ
Problem 1 Let Xi, ,Xn be a random sample from a Normal distribution with mean μ and variance 1.e Answer the following questions for 8 points total (a) Derive the moment generating function of the dis...

Problem 1 Let Xi, ,Xn be a random sample from a Normal distribution with mean μ and variance 1.e Answer the following questions for 8 points total (a) Derive the moment generating function of the distribution. (1 point). Hint: use the fact that PDF of a density always integrates to 1. (b) Show that the mean of the distribution is u (proof needed). (1 point) (c) Using random sample X1, ,Xn to derive the maximum likelihood estimator of μ (2...

Let Xi., Xn be a random sample from the distribution with density f(r, θ)-303/2.4 for x > θ and 0 otherwise. Determine the MLE of θ and derive 90% central CI interval for θ. If possible find an ex...

Let Xi., Xn be a random sample from the distribution with density f(r, θ)-303/2.4 for x > θ and 0 otherwise. Determine the MLE of θ and derive 90% central CI interval for θ. If possible find an exact CI. Otherwise determine an approximate CI. Explain your choice Let Xi., Xn be a random sample from the distribution with density f(r, θ)-303/2.4 for x > θ and 0 otherwise. Determine the MLE of θ and derive 90% central CI interval...

4. Let Xi, . . . , xn be a random sample from the inverse Gaussian...

Homework Answers