1) Xi~Bernoulli(p), MLE and MOME of p 2) Xi~Exp(λ), MLE and MOME of λ 3) Xi~Normal(μ,...

1) Xi~Bernoulli(p), MLE and MOME of p

2) Xi~Exp(λ), MLE and MOME of λ

3) Xi~Normal(μ, σ² ), MLE and MOME of μ, σ²

Expert Solution

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orchestra answered 1 year ago

a) Find the analytic MLE formula for exponential distribution exp(λ). Show that MLE is the same...

a) Find the analytic MLE formula for exponential distribution exp(λ). Show that MLE is the same as MoM estimator here. (b) A random sample of size 6 from the exp(λ) distribution results in observations: 1.636, 0.374, 0.534, 3.015, 0.932, 0.179. Find the MLE on this data set in two ways: by numerical optimization of the likelihood and by the analytic formula. For (b): please give both values from the analytic MLE formula and numerical MLE solution on this data set....

Find the (probability generating function) p.g.f.’s of the following distributions:[3+3=6] •P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,...,...

Find the (probability generating function) p.g.f.’s of the following distributions:[3+3=6] •P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,..., and λ >0. •P(X=x) =((pq)^x)(1−q^(N+1))^−1,for x= 0,1,..., N; where 0 < p < 1, p+q= 1.

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y =...

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Consider a random sample of size n= 20 from Xi~Exp(2). Find exact P(X bar > 2.59)....

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Taylor series f(xi+1)=f(xi)+f'(xi)h+(f''(xi)/2!)h2+(f'''(xi)/3!)h3+..... given f''(xi)=(-f(xi+3)+4f(xi+2)-5f(xi+1)+2f(xi))/h2 what is the order of error o(h2)

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Normal mu 722 sigma 189 xi P(X<=xi) 151 0.0013 263 0.0076 532 0.1574 721 0.4979 810...

Normal mu 722 sigma 189 xi P(X<=xi) 151 0.0013 263 0.0076 532 0.1574 721 0.4979 810 0.6793 961 0.8970 P(X<=xi) xi 0.11 490.1862 0.12 499.9275 0.24 588.5088 0.31 628.2843 0.38 664.2641 0.76 855.4912 0.89 953.8138 Use the cumulative normal probability excel output above (dealing with the amount of money parents spend per child on back-to-school items) to answer the following question. The probability is 0.38 that the amount spent on a randomly selected child will be between two values (in...

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