please answer number 2 Let X₁, ...., Xn; i = 1,2,..., n is a random sample from thepopulation with the probability mass function:f (x|0) = 0 (1 - 0)* ; x = 0,1,2,... 0 <0 < 1if it is known that parameter 0 has a prior beta probabilityfunction (3;4) as follows:T(7)h(0) = T(3)r (4)1. determine the likelihood function L(x|0)2. find the density function with X and 0, i.e. g(x|8)3. find the posterior distribution for 0, i.e. k(0|x)4. find the Bayesian estimator for 0, that is, T0² (1-0)³ ; 0 <0 <1

Geometric distribution is a discrete probability mass function that represents the probability of…

Answered: Let X₁, ...., X₁; i = 1,2, ... , n is a…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).
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Let X1, . . . , Xn i.i.d. U([θ1, θ2]), i.e., X1, . . . , Xn are independent and follow a uniform distribution on the interval [θ1, θ2] for θ1, θ2 ∈ R and θ1 < θ2. Find an estimator for θ1 and θ2 using the method of moments.
2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.
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An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for (Χ,Y ) is given by the following table: X Y K100 K250 K0 0.20 0.05 K100 0.10 0.15 K200 0.20 0.30 Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance. Find the probability that a randomly selected policy holder has a home deduction of at least K100. Are the random variables Χ and Y independent? Explain your answer. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected…

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