2

Let XiXn be an ii.d. sample from distribution with density function f(c; 0) = %r20-se-*/ , for € > 0. Hint: Using wolfram alpha, E(X) = 38 and E(X? _ 1202 ...

Question

Let XiXn be an ii.d. sample from distribution with density function f(c; 0) = %r20-se-*/ , for € > 0. Hint: Using wolfram alpha, E(X) = 38 and E(X? _ 1202 1. (Spts) Differentiate the log-likelihood function to find the score; and the MLE for &.2. (Zpts) Calculate the variance of the score function to get the Fisher information In (0) and the Cramer-Rao lower bound. 3. (Spts) Calculate the expected value and variance of the MLE: Based on that; is the MLE an efficient estimator?

Let Xi Xn be an ii.d. sample from distribution with density function f(c; 0) = %r20-se-*/ , for € > 0. Hint: Using wolfram alpha, E(X) = 38 and E(X? _ 1202 1. (Spts) Differentiate the log-likelihood function to find the score; and the MLE for &. 2. (Zpts) Calculate the variance of the score function to get the Fisher information In (0) and the Cramer-Rao lower bound. 3. (Spts) Calculate the expected value and variance of the MLE: Based on that; is the MLE an efficient estimator?



Answers

Let $Y_{1}, Y_{2}, \ldots, Y_{n}$ denote a random sample from the density function given by $$f(y | \theta)=\left\{\begin{array}{ll}\left(\frac{1}{\theta}\right) r y^{r-1} e^{-y^{\prime} / \theta}, & \theta>0, y>0 \\0, & \text { elsewhere }\end{array}\right.$$ where $r$ is a known positive constant. a. Find a sufficient statistic for $\theta$ b. Find the MLE of $\theta$ c. Is the estimator in part (b) an MVUE for $\theta$ ?

Hello. This is problem 9.83. We're going to deport a so we have a uniformly distributed uh random variable um and it's made up of wise. So firstly we need to find the likelihood, we're trying to find the Emily of data. So the likelihood of data is equal to the product of eyes. You could want to end of one over tooth data plus one. And this is the important part right here. Those brackets. So it's gonna be from zero 12 0 is less than ricotta wise, java, Which is less than or equal to two times data plus one. So this is just given us our domain at least of just one why? But now it's all of the wise. Okay so we're trying to maximize this. So um so we'll do one right? Because just 12 then it's one and then the concepts too, Times Data Plus one. We're going to exponentially ate it so too then um but now uh we need to see well when does this work? So we could just write down, okay I put a one here. And so this only works when zero is less than or equal to wise of them. She lives in our equal to two Times Data Plus one. Um So then you must be thinking what's going on here? So you want uh the numerator to be the biggest and then the biggest that he could be is if you get the maximum of the wise which is this was then um But we're not done yet so it's not wiser than the biggest. We need to do a little algebra. Uh Because what we're trying to maximize uh data. So from here we could just write down the same thing one over two times data plus 1 to the end. And then what is this called indicator function? So if you were to um subtract one and divide by two on both sides, you get negative. Uh huh. Is less than or equal to worry. So then mine is one give other way too which is less than or equal to data. So this right here would be the biggest event. So now we could just write down the Emily. So Emily of data is theater. Uh huh. Which is equal to wise event. Maya is one all over to. Okay now we need to find the Emily of the variance. So her p we know that the variants. Why Is he grew one or 12 times two data plus one square by definition and the Emily uh variants. So why is so one of the toe stays the same? Is there for me too? Times whatever data is. So instead of the theater we write down the theater. Huh Too multiplied by wise event one is one divided by two plus one. We're going to square this simplifying. We'll get wiser men squared or 12


Similar Solved Questions

5 answers
ERcobPmuous Arteaunts wrill be ccoupied ( the rent Is $910 per month markct survey suggcsts [hat; averene Tnn Maneclr 100-unit apartnent complex knois from experencc Wnatrershoulothe manaoct Cargc maxi mlze revcnuc? additonal unit will remaln vacant tor nach <i0 incmcisc Dr MoninlPrinttou? natutaOlvcn cquatin: (Rjurd Yovr naloHmnOonndl#PoroximationNuuton nncnod *ilrspecificd Inlual aporoximationplucea
ERcob Pmuous Artea unts wrill be ccoupied ( the rent Is $910 per month markct survey suggcsts [hat; averene Tnn Maneclr 100-unit apartnent complex knois from experencc Wnatrershoulothe manaoct Cargc maxi mlze revcnuc? additonal unit will remaln vacant tor nach <i0 incmcisc Dr Monin l Printtou? na...
5 answers
Let G Ie graph with vertices Ad MOSL %,elges. Prove that its chromatic Wer is
Let G Ie graph with vertices Ad MOSL %, elges. Prove that its chromatic Wer is...
5 answers
Scme bacteria can move away from light: This is callednegative phototaxispositive chemotaxisataxisnegative chemotaxispositive phototaxisQuestion 6Prokaryotic and eukaryotic flagella are analogous structures a5 they are not derived from shar ancestor:FalseTrue
Scme bacteria can move away from light: This is called negative phototaxis positive chemotaxis ataxis negative chemotaxis positive phototaxis Question 6 Prokaryotic and eukaryotic flagella are analogous structures a5 they are not derived from shar ancestor: False True...
5 answers
Balance the following reactions by placing coefficients in the blanks:Cr04?-(aq) CrOz (aq)HSNO2 (aq) + 1HzO()->HSnO3 (aq)OH-KMnO4(aq) MnO2(s)NaNO2(aq) 1H20() 7 NaNO3(aq)KOH(aq)
Balance the following reactions by placing coefficients in the blanks: Cr04?-(aq) CrOz (aq) HSNO2 (aq) + 1HzO()-> HSnO3 (aq) OH- KMnO4(aq) MnO2(s) NaNO2(aq) 1H20() 7 NaNO3(aq) KOH(aq)...
5 answers
Find the first partial derivatives of the function_ fx, Y) = 2x + by cX + cyfx(x,Y) =Mx,Y) =
Find the first partial derivatives of the function_ fx, Y) = 2x + by cX + cy fx(x,Y) = Mx,Y) =...
5 answers
The Laplace Translorm Y(s) ol Ihe IVP Y4y-65O) =Y (0) = _1iS given by(8 - 31(92 48) ( + 1)(8? _ 49) 8 _Tnke False
The Laplace Translorm Y(s) ol Ihe IVP Y4y-6 5O) = Y (0) = _1iS given by (8 - 31(92 48) ( + 1)(8? _ 49) 8 _ Tnke False...
5 answers
Given the ordered pairs for the initial and terminal points of each vector; are the two vectors equivalent?A(3, 1), B(O, 3), C(-4,,2), D(-1,-1) AB DcSelect one: A YesB. No
Given the ordered pairs for the initial and terminal points of each vector; are the two vectors equivalent? A(3, 1), B(O, 3), C(-4,,2), D(-1,-1) AB Dc Select one: A Yes B. No...
5 answers
H2.10 1eve Homework UnanswieredWhat will be the name of the following compound?Sclect an answcrand submit, Forkeyboard navigatlion, usethe downaino "e sclectanswet(Z)-2-pentene(Z)-3-pentene(E)-2-pentena~pentene(E)-3-cyclopenten?
H2.10 1eve Homework Unanswiered What will be the name of the following compound? Sclect an answcrand submit, Forkeyboard navigatlion, usethe downaino "e sclect answet (Z)-2-pentene (Z)-3-pentene (E)-2-pentena ~pentene (E)-3-cyclopenten?...
1 answers
Suppose that $F$ is a complete ordered field, so that there is an isomorphism $f$ from $\mathbf{R}$ to $F .$ Show that there is actually only one isomorphism from $\mathbf{R}$ to $F .$ Hint: In case $F=\mathbf{R},$ this is Problem $3-17 .$ Now if $f$ and $g$ are two isomorphisms from $\mathbf{R}$ to $F$ consider $g^{-1} \circ f.$
Suppose that $F$ is a complete ordered field, so that there is an isomorphism $f$ from $\mathbf{R}$ to $F .$ Show that there is actually only one isomorphism from $\mathbf{R}$ to $F .$ Hint: In case $F=\mathbf{R},$ this is Problem $3-17 .$ Now if $f$ and $g$ are two isomorphisms from $\mathbf{R}$ to...
5 answers
The following parts are considered in the Tyz-space, Rs, and the cy-plane corre- sponds to the plane of 2 = 0. (a) Consider the plane x + 2y + 2 = 10 as a graph of 2 = f(w,y). Use surface integral to calculate the area for the part of the plane which sits over the unit disk centred at the origin in the Ty-plane; that is D = {(€,y) | x2 +y? < 1}.
The following parts are considered in the Tyz-space, Rs, and the cy-plane corre- sponds to the plane of 2 = 0. (a) Consider the plane x + 2y + 2 = 10 as a graph of 2 = f(w,y). Use surface integral to calculate the area for the part of the plane which sits over the unit disk centred at the origin in ...
5 answers
Is the following language decidable? Prove youranswer. L={〈M〉|M is a Turing machine that accepts exactly 5 strings}L={〈M〉|M is a Turing machine that accepts exactly 5 strings}First statewhether LL is decidable or undecidable,then prove your answer.
Is the following language decidable? Prove your answer. L={〈M〉|M is a Turing machine that accepts exactly 5 strings}L={〈M〉|M is a Turing machine that accepts exactly 5 strings} First state whether LL is decidable or undecidable, then prove your answer....
5 answers
Please answer the question in the picture below. This is relatedto Measure Theory (Lebesgue Measure).
Please answer the question in the picture below. This is related to Measure Theory (Lebesgue Measure)....
5 answers
Given;P(A)=0.7 and P(A and B)=0.5. What is P(B) ifAand Bare _independent?0.3500.7140.2000.12
Given; P(A)=0.7 and P(A and B)=0.5. What is P(B) ifAand Bare _independent? 0.350 0.714 0.200 0.12...
5 answers
Following Rrph this cqullibnumculculale the enthalpy (BH}Keqv. 1T Loppur IIn Ammonia Equilbrium6ctr10794x - 65.282nretprocel KelianshShow your colculationg hcreDH =kilojoules Imolethe reaction cndolhennic exothenic in the forward direction? Bascd upon this dalaWhat will huppcn "incrcased? equilibrium ifthe (emperatureOnen
following Rrph this cqullibnum culculale the enthalpy (BH} Keqv. 1T Loppur IIn Ammonia Equilbrium 6ctr 10794x - 65.282 nretprocel Keliansh Show your colculationg hcre DH = kilojoules Imole the reaction cndolhennic exothenic in the forward direction? Bascd upon this dala What will huppcn " incrc...

-- 0.023086--