Consistency of Maximum likelihood estimator: Let {Xi}ni=1 be n i.i.d. random variables with normal distribution N(θ, θ), for some unknown θ > 0. Compute the maximum likelihood estimator of θ and show that it is consistent.

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Q: The joint probability distribution of thr random variables X and Y is given below: f(x,y) =   cxy ,…

A: Given : fx, y = cxy     ; 0<x<2, 0<y<x0        ;  otherwise  a. value of constant c ,…

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A: *Answer:

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A: (i) Using Central limit theorem,  X¯~Nλ^, λ^n Therefore, PQ=λ^-λλ^n~N0,1

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A: Given:

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A: Reviewing information, Y~binomial(n,θ)f(y)=ny θy (1-θ)n-y                     ; y=0,1,......,n0…

Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Solution-: We have following table:   Y=1 Y=2 Y=3 Total X=1 - 0.08 - 0.20 X=2 - 0.32 - 0.80…

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A: Problem can be solved using the concept of maximum likelihood and minimum variance estimator. as…

Q: Let X1, X2, X, be a random sample from a Bernoulli distribution with parameter p. a) Find a moment…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

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Q: Suppose that Xi,i =1,2,...,n have an Exponential distribution with parameter delta. a) Find maximum…

A: To get the maximum likelihood estimator, we maximize the likelihood function. To an estimator T be…

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A: Let Y1, Y2, . . . , Yn be independent and identically distributed random variables such that for…

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A: Given:- X1, X2,.....Xn are random samplePX=1 = P1PX=2 = P2PX=3 =1-P1-P2

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A: Solution:

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A: 1 (i)…

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Q: 17. Let (y1, Y2, ..., Yn) be a random sample from a normal distribution such that E(y;) = a + Bxi,…

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Q: b) Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = kx², 0…

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A: The following information is given in the question X 0 1 P(x) 0.4 0.6 Now, Since X1 and X2…

Q: Let X1, X2, .., Xn be a random sample from a Bernoulli distribution: p(x; 0) = 0*(1 – 0)1-*. We wish…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

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Q: 4. Given a simple random sample {X,}" - N(H,0²), then has SIn A. normal distribution В.…

A: Here, (X-bar -µ)/(s/n) follows a t distribution.

Q: 1 f(x) = 1 exp - 2 2.

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Q: The probability of the number of salaried employee participant in an optional retirement program is…

A: It is given that n=4 and p=0.4.

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A: Solution

Q: Consistency of Maximum likelihood estimator: Let {Xi}ni=1 be n i.i.d. random variables with…

A: Suppose that the random variables X1, · · · , Xn form a random sample from a distributionf(x|θ); if…

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A: The answer can be given using probability distribution properties. I have attached step by step…

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Q: Let X1,..., Xn a random sample with distribution f (x; 0) = (0 + 1)a", 0 -1. (а). Find the method of…

A: @solution::::

Q: (b) Find the likelihood function for A, L(A, x). (c) Hence, find the log-likelihood and show that…

A: Given that the random variable X has a continuous distribution with parameter λ&gt;0 and the…

Q: A continuous random variable X has cumulative distribution function F(x) = 1.5 3 2 6 –1 < x < 1. a)…

A: (a) To evaluate the expectation by definition, we need to derive probability density function first,

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.