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# Let Xi,Xz, variables isXn "4 Exponential(8). The probability density function for these randomf(r18)e-5 , 1 > 0; 8 > 0.Find the maximum likelihood estima...

## Question

###### Let Xi,Xz, variables isXn "4 Exponential(8). The probability density function for these randomf(r18)e-5 , 1 > 0; 8 > 0.Find the maximum likelihood estimator for 8.b. Compare the MLE to the estimator 8 (Xi + Xn)/2. Which do you recommend? Explain. You can use the following facts: E(X;) = 8 and Var(X;) = 82 , for anyConstruct a 100(1 _ a)% C.I. for B using the pivotal quantity (2nBxLe) /8. You can use the fact that (2nBuLe) /8 xn=Is 1/8 MLE unbiased for 1/82 Prove youT claim. You ca

Let Xi,Xz, variables is Xn "4 Exponential(8). The probability density function for these random f(r18) e-5 , 1 > 0; 8 > 0. Find the maximum likelihood estimator for 8. b. Compare the MLE to the estimator 8 (Xi + Xn)/2. Which do you recommend? Explain. You can use the following facts: E(X;) = 8 and Var(X;) = 82 , for any Construct a 100(1 _ a)% C.I. for B using the pivotal quantity (2nBxLe) /8. You can use the fact that (2nBuLe) /8 xn= Is 1/8 MLE unbiased for 1/82 Prove youT claim. You can use the facts Xi-IXX; Gamma(n, 8) and E [(Ei-1X;)*] (8*T(n + k)) /T(n) when ~n and Ci-IX; Gamma(n, B).  #### Similar Solved Questions

##### Mnte the equauoneexponcntial(Senenb)10g10z44 = ;noponnm equation of the asymptote:function Write" hertamaln rnA Chooectne grph of the f(x) = 3*Dom ut:Range;Asymptote:expression without using calculator: ( paints} Simplify the logarithmiclogs 81
mnte the equauone exponcntial (Senenb) 10g10z44 = ; noponnm equation of the asymptote: function Write" hertamaln rnA Chooectne grph of the f(x) = 3* Dom ut: Range; Asymptote: expression without using calculator: ( paints} Simplify the logarithmic logs 81...
##### Problem 5 A system consists of three independent components, 4, B and C, connected in a series. The lifespans of components A B, and C have an exponential distribution with parameters 0.2, 0.1, and 0.15 (days)-1 (equivalently, means 5, 10, and 1/0.15 days) The system fails when one of the components fails. a) Find the probability that the component whose failure caused the system to fail is component C (b) You can increase the expected lifespan of one of the components by day: Which component sh
Problem 5 A system consists of three independent components, 4, B and C, connected in a series. The lifespans of components A B, and C have an exponential distribution with parameters 0.2, 0.1, and 0.15 (days)-1 (equivalently, means 5, 10, and 1/0.15 days) The system fails when one of the components...
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Some equilibrium solutions (15) Determine the equilibrium temperature distribution for one-dimensional rod of length L with the following boundary conditions: du u(0) = 0, (L) =a dx Du (0) = 0, "(L) = a Dâ‚¬ du Du (0) u(o) = 4 _ (L) = 8 dr dr...
##### Scores BMCC fall 2017 MATISO 5 department final exam form _ HmIai distribution with = mean of 70 and ctanderd deviation of 8, Wnat percenl of the population has following?score Lrealet than 90score between 60 and 85score Icss than 60population of a city normally distributed with & mean age 38 and = standard deviation of 4 2. Find the probability that & person chosen rndom betwcen 30 and Suppose popullion of the city J000,000. How WA people are betwecn 30 and 407
Scores BMCC fall 2017 MATISO 5 department final exam form _ HmIai distribution with = mean of 70 and ctanderd deviation of 8, Wnat percenl of the population has following? score Lrealet than 90 score between 60 and 85 score Icss than 60 population of a city normally distributed with & mean age 3...
##### 10. (10 marks Consider Uniform random variable random vanable 1000VE(2 Mans the variarice of X marks) What PIX > 125 X < 50017vli Ine interva20). Consider another
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##### The upper triangular matricesandareinverse tO each other What IS a?
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##### Use the Rcot Testto Cetermine Khether thc seres Eneni Dover Denl 2G) [denulyEvzluate t2tolidttiro Umas V1ojSincs1al p~~Ct[-/2 Points]DETAILSSCALC8 11.10.011.Mi:Fndnn Maclaririn Berlns (ot {{) using Lhe del nition oi 2 Michjun a2h2 =powvnr estic? Expal:ionDa norinow tiet'asjucatrd moeconteroen t
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##### Let $n$ be a prime number and let $a_{1}, a_{2}, ldots, a_{m}$ be positive integers. Consider $f(k)$ the number of all $m$ -tuples $left(c_{1}, ldots, c_{m}ight)$ satisfying $1 leq c_{i} leq a_{i}$ and $sum_{i=1}^{m} c_{i} equiv k(mod n) .$ Show that $f(0)=f(1)=cdots=f(n-1)$ if and only if $n mid a_{j}$ forsome $j in{1, ldots, m}$
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##### For each of the following premises, what relevant conclusion can be drawn? Use the rules of inference to obtain the conclusion from the premises."Every student has an Internet account" "Homer does not have an Internet account:' "Maggie has an Internet account'Let:S = "Every student has an Internet account' D = "Homer does not have an Internet account' T= "Maggie has an Internet account'
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##### AtalaLt ~Weeri Il Ient Jedi Utl IrLET Hnle Ma WimIieKeaIueloh {04 Fou (6, 6)
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##### If C is the circle of radius 3 centered at the origin, starting at the point (3,0) and moving around once in the counter-clockwise direction; evaluate the line integral:Jc 2 ydx cy? dy
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##### Establish each identity. $$\frac{\cos (2 \theta)}{1+\sin (2 \theta)}=\frac{\cot \theta-1}{\cot \theta+1}$$
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##### The following data was collected to explore how the averagenumber of hours a student studies per night and the student's GPAaffect their ACT score. The dependent variable is the ACT score,the first independent variable (x1) is the number of hours spentstudying, and the second independent variable (x2) is the student'sGPA. ACT Score Study Data Study Hours GPA ACT Score 1 2 17.79 1 219.68 2 2 25.56 2 3 27.83 2 4 30.48 A regression Analysis has beenperformed to estimate the model and the
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##### A geological disturbance in San Andreas fault generated a seismic wave that was detected in Phoenix, AZ, approximately 1000 km from the epicenter. If such waves travel at an average speed of 6.5 km/s, what would be the time-lag between the disturbance and the detection? How does this speed compare with that of sound waves in air at a day temperature of 239C?2.6 min, Vsetsmic / sound ~ 193.2 min; Vsetsmic/ Vsound 212.6 min;, Vselsmic/ Vsound ~ 262.9 min, Vseismic/ Vsound ~ 29
A geological disturbance in San Andreas fault generated a seismic wave that was detected in Phoenix, AZ, approximately 1000 km from the epicenter. If such waves travel at an average speed of 6.5 km/s, what would be the time-lag between the disturbance and the detection? How does this speed compare w...