Let Y1,...,Yn be a sample from the density f(y) = 3y2/θ3,0 ≤ y ≤ θ. Calculate the mean of this distribution and find the Method of Moments estimate of θ.
Let Y1,...,Yn be a sample from the density f(y) = 3y2/θ3,0 ≤ y ≤ θ. Calculate...
Let Y1,Y2, …… Yn be a random sample from the distribution f(y) = θxθ-1 where 0 < x < 1 and 0 < θ < ∞. Show that the maximum likelihood estimator (MLE) for θ is
Let Y1, Y2, ..., Yn denote a random sample from an exponential distribution with mean θ. Find the rejection region for the likelihood ratio test of H0 : θ = 2 versus Ha : θ ≠ 2 with α = 0.09 and n = 14. Rejection region =
1. Let Y1, . . . ,Y,, be a random sample from a population with density function 0, otherwise (a) Find the method of moments estimator of θ (b) Show that Yan.-max(Yi, . . . ,%) is sufficient for 02] (Hint: Recall the indicator function given by I(A)1 if A is true and 0 otherwise.) (c) Determine the density function of Yn) and hence find a function of Ym) that is an unbiased estimator of θ (d) Find c so...
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a population with Rayleigh distribution (Weibull distribution with parameters 2, θ) with density function f(y|θ) = 2y θ e −y 2/θ, θ > 0, y > 0 Consider the estimators ˆθ1 = Y(1) = min{Y1, Y2, · · · , Yn}, and ˆθ2 = 1 n Xn i=1 Y 2 i . ii) (10 points) Determine if ˆθ1 and ˆθ2 are unbiased estimators, and in...
10. Let Y1,..., Y, be a random sample from a distribution with pdf 0<y< elsewhere f(x) = { $(0 –» a) Find E(Y). b) Find the method of moments estimator for 8. c) Let X be an estimator of 8. Is it an unbiased estimator? Find the mean square error of X. Show work
1. (a) Let Yi,... , Yn be a random sample from a distribution with mean θ and finite variance σ2. Find the BLUE of θ and justify that it is, in fact, the Best Linear Unbiased Estimate. sample variance. 1. (a) Let Yi,... , Yn be a random sample from a distribution with mean θ and finite variance σ2. Find the BLUE of θ and justify that it is, in fact, the Best Linear Unbiased Estimate. sample variance.
5. Consider a random sample Y1, . . . , Yn from a distribution with pdf f(y|θ) = 1 θ 2 xe−x/θ , 0 < x < ∞. Calculate the ML estimator of θ. 6. Consider the pdf g(y|α) = c(1 + αy2 ), −1 < y < 1. (a) Show that g(y|α) is a pdf when c = 3 6 + 2α . (b) Calculate E(Y ) and E(Y 2 ). Referencing your calculations, explain why M1 can’t be...
Let Y1 , Y2 , . . . , Yn denote a random sample from the uniform distribution on the interval (θ, θ+1). Let a. Show that both ? ̂1 and ? ̂2 are unbiased estimators of θ.
Problem 2.1. Let Y1, ...,Yn be a random sample from a uniform distribution on the interval [0 – 1,20 + 1]. a. Find the density function of X = Y;-0 (note that Yi ~ Uf0 - 1,20 + 1]). b. Find the density function of Y(n) = max{Y;, i = 1,...,} c. Find a moment estimator of . d. Use the following data to obtain a moment estimate for 4: 11.72 12.81 12.09 13.47 12.37.
. Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ > 6? If so, what is the . Let Yi.... Yn be a random sample from a distribution with the density function 393 fe(y) =- Is there a UMP test at level α for testing Ho : θ test? vs. Hi : θ >...