(c) Find A, the maximum likelihood estimator for A. (You do not need to prove that your solutionis a max).(d) Show that your estimator X from (c) is an unbiased estimator of X. Let X1, X2, X3, and X4 be independent Poisson random variables, with parametersA₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively.(a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4).(b) Find L(A) and (A), the likelihood and log-likelihood functions.

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Answered: Let X1, X2, X3, and X4 be independent…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?
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A random variable X has a N(0,1) distribution. Use the moment generating function of X to compute (a) the third and (b) fourth moments of X, i.e., E(X³) and E(X4).
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Let X be a random variable with pmf P(O)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b) Find F(1.3). (c) Find F(3).
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Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn
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Consider an AR(2) model: STEPS; -Write the equation of the AR(2) model- Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.- Assume that there is an initial value of the returns, denoted by $r_0$, and we have the AR(2) model at time rt, convert the AR(2) model into its equivalent MA(t)
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Let X1, X2, X3, and X4 be independent Poisson random variables, with parameters A₁ = 3A, A2 = A, A3 = 9A, and A4 = 4A, respectively. (a) Find and simplify the joint pmf f(x1, x2, x3, x4; A1, A2, A3, A4). (b) Find L(A) and (A), the likelihood and log-likelihood functions.