3

# (10 points) (10.3.4 from Probability and Statistical Inference) Suppose that Xi, Xn are iid Uniform(0,0) given that 0 where the parameter 0 is unknown. Suppose tha...

## Question

###### (10 points) (10.3.4 from Probability and Statistical Inference) Suppose that Xi, Xn are iid Uniform(0,0) given that 0 where the parameter 0 is unknown. Suppose that has prior distribution Pareto(a , 8) , which has pdf _ given by h(0) Ba' 0-(5+1)1{a 0} where &, 8 are known positive numbers. Recall the sufficient statistic T' X(n) max{X,. X} which is the largest order statistic. (a) Show that the posterior distribution of 0 given x = {21,12, Tn turns out to be Pareto(a' max(t,

(10 points) (10.3.4 from Probability and Statistical Inference) Suppose that Xi, Xn are iid Uniform(0,0) given that 0 where the parameter 0 is unknown. Suppose that has prior distribution Pareto(a , 8) , which has pdf _ given by h(0) Ba' 0-(5+1)1{a 0} where &, 8 are known positive numbers. Recall the sufficient statistic T' X(n) max{X,. X} which is the largest order statistic. (a) Show that the posterior distribution of 0 given x = {21,12, Tn turns out to be Pareto(a' max(t,a), 8' = n + 8), where T = t = max{T1, Infa (b) What is the Bayes estimator for 0? (c) Suppose 10, Xn 1.5, a =4, 8 = 20. What is the posterior probability of Ho 0 < 22

#### Similar Solved Questions

##### Write the first five terms of the recursively defined sequence8, a +1 an + 2The first five temms of the sequence are 81 =L,a2 = (Simplify your answer Type an integer r simplified fraction_and a5
Write the first five terms of the recursively defined sequence 8, a +1 an + 2 The first five temms of the sequence are 81 =L,a2 = (Simplify your answer Type an integer r simplified fraction_ and a5...
##### How would you make 1 L of a 25% solution of ethanol (a liquid, formula weight 44) in water?
How would you make 1 L of a 25% solution of ethanol (a liquid, formula weight 44) in water?...
##### (b) 50 mm diameter hydraulic cylinder is directly under the foot pedal hydraulic jack If a person with mass of 100 kg places all their weight onto the pedal, what is themaximum pressure that_can be_developed in _the hydraulic fluid in the cylinder? Assume g 9.81 m/s?, Work in base SI units_ State vour answer in kPa (20 marks)
(b) 50 mm diameter hydraulic cylinder is directly under the foot pedal hydraulic jack If a person with mass of 100 kg places all their weight onto the pedal, what is themaximum pressure that_can be_developed in _the hydraulic fluid in the cylinder? Assume g 9.81 m/s?, Work in base SI units_ State ...
##### A bowling ball is dropped at the same moment as a soccer ball: Which of the following statements is false?Both will strike the ground at the same timeBoth have the same force of gravity:Both have the same velocity before impact:Both have the same acceleration:
A bowling ball is dropped at the same moment as a soccer ball: Which of the following statements is false? Both will strike the ground at the same time Both have the same force of gravity: Both have the same velocity before impact: Both have the same acceleration:...
##### The general solution of the equation y(3) 25y' = 0cos(5 t) + bt cos(5t) + pb) cos(5 t) + b t cos(5t) + ptcos(5 t) + b sin(5 t)cos(5 t) + b sin(5 t) + p
The general solution of the equation y(3) 25y' = 0 cos(5 t) + bt cos(5t) + p b) cos(5 t) + b t cos(5t) + pt cos(5 t) + b sin(5 t) cos(5 t) + b sin(5 t) + p...
##### Extra Credit: [5 points] Explain in detail how magnesium nucleus that was made from antimatter instead of normal matter would behave in the ahove problem is everything else remained the same_
Extra Credit: [5 points] Explain in detail how magnesium nucleus that was made from antimatter instead of normal matter would behave in the ahove problem is everything else remained the same_...
##### CRYSTALLIZATION AND MELTING POINTS PrncplesCrystallization (which i5 sometimes Galled "bractional cryslllization" or "recrystallization") is used t0 separate mixtures of solids It can be used to purify solid substances. Punfication is a special type of separation; the compound t0 be purified i5 separated from the "impurities"In crystallization, the chemist separates substances by taking advantage of differences in solubility. This can be seen by thinking = about the
CRYSTALLIZATION AND MELTING POINTS Prncples Crystallization (which i5 sometimes Galled "bractional cryslllization" or "recrystallization") is used t0 separate mixtures of solids It can be used to purify solid substances. Punfication is a special type of separation; the compound t...
##### Consider the following hypothetical findings on the evaluation of screening test for tuberculosis: 40 diseased and positive individuals; 15 diseased and negative individuals, 75 nol = diseased and positive individuals; 1,600 not diseased and negative individuals How would you interpret the negative predictive value of the screening test for tuberculosis? About 9696 of peopl without tuberculosis tested negative Among people who tested negative, nearly 9900 did not have tuberculosis Approximately
Consider the following hypothetical findings on the evaluation of screening test for tuberculosis: 40 diseased and positive individuals; 15 diseased and negative individuals, 75 nol = diseased and positive individuals; 1,600 not diseased and negative individuals How would you interpret the negative ...
##### (Zpts) For what value of a it holds f(3r + ln(2 + e' ))dr = a(r + 9z+z) + C where â‚¬ is the nstant of integration and we assume r â‚¬ R ?
(Zpts) For what value of a it holds f(3r + ln(2 + e' ))dr = a(r + 9z+z) + C where â‚¬ is the nstant of integration and we assume r â‚¬ R ?...
##### Statement-1: $frac{sin (A+B)+sin (A-B)}{cos (A+B)+cos (A-B)}=an A$Statement-2: $sin (A+B)+sin (A-B)=2 sin A$$cos (A+B)+cos (A-B)=2 cos A$
Statement-1: $frac{sin (A+B)+sin (A-B)}{cos (A+B)+cos (A-B)}= an A$ Statement-2: $sin (A+B)+sin (A-B)=2 sin A$ $cos (A+B)+cos (A-B)=2 cos A$...
##### 10 ptsQuestion 5Ger #-4d1 Il15 pcnty] Remnte the integrand a5 & fux traction You will be graded on the detoils of this stzp:Sprtq61 Determene tne indehrate integral Ndte Cedt wlbe slel aen n the written work ofthe written analysis (all of the mathematical stratan  Itesuts are onl bosed upon graphs or numerical tables you wil be given @ zerq; AJ #ork IUt te atitten OUL Cokculus processes; dlgebraic Gol Sxeps mthout work Will csimplifications arithmetic etc must shown in Iresult ina lo
10 pts Question 5 Ger #-4d1 Il 15 pcnty] Remnte the integrand a5 & fux traction You will be graded on the detoils of this stzp: Sprtq 61 Determene tne indehrate integral Ndte Cedt wlbe slel aen n the written work ofthe written analysis (all of the mathematical stratan  Itesuts are onl bose...
##### A long narrow slit $0.10 \mathrm{mm}$ wide is illuminated by light of wavelength 500 nm coming from a point source 0.90 m away. Determine the irradiance at a point $2.0 \mathrm{m}$ beyond the screen when the slit is centered on, and perpendicular to, the line from the source to the point of observation. Write your answer in terms of the unobstructed irradiance.
A long narrow slit $0.10 \mathrm{mm}$ wide is illuminated by light of wavelength 500 nm coming from a point source 0.90 m away. Determine the irradiance at a point $2.0 \mathrm{m}$ beyond the screen when the slit is centered on, and perpendicular to, the line from the source to the point of observat...
##### Why are the secretions of the male reproductive glands so important to sperm?
Why are the secretions of the male reproductive glands so important to sperm?...
##### Look at the caesium chloride crystal structure on WWW dawgsdk org/crystal: The crystal binding energy in solid CstCl is almost entirely due to the ionic interactions. By examining a sketch of the structure extended to eight cubic unit cells (i.e. all of the unit cells which share one corner), plus the next set of ions adjacent to the faces of that cube, calculate for each type of neighbouring ion, up to 2a away, where a is the cubic unit cell edge length, the distance from the central ion, and t
Look at the caesium chloride crystal structure on WWW dawgsdk org/crystal: The crystal binding energy in solid CstCl is almost entirely due to the ionic interactions. By examining a sketch of the structure extended to eight cubic unit cells (i.e. all of the unit cells which share one corner), plus t...
##### Pt) A cell of some bacteria divides into two cells every 40minutes. The initial population is 3lbacteria.(a) Find the size of the population after hours y(t) (function of d(b) Find the size of the population after 3 hours 9(3)(c) When will the population reach 9k T =
pt) A cell of some bacteria divides into two cells every 40minutes. The initial population is 3lbacteria. (a) Find the size of the population after hours y(t) (function of d (b) Find the size of the population after 3 hours 9(3) (c) When will the population reach 9k T =...
##### Under the null hypothesis of independence; compute the expected count of the number of people living Kentucky who oppose spending additional tax dollars light rail infrastructure. 3 pts:)How many degrees of freedom does the test statistic Xobs have? (2 pts:)What is the critical valuc for this hypothesis test?pts: )For this hypothesis test, the test statistic Xobs 9.964_ Basecl on this_ indicate the result of the test (reject Ho or fail t0 reject Ho) #udl state your corclusion the context o
Under the null hypothesis of independence; compute the expected count of the number of people living Kentucky who oppose spending additional tax dollars light rail infrastructure. 3 pts:) How many degrees of freedom does the test statistic Xobs have? (2 pts:) What is the critical valuc for thi...