Let Y1, ..., Yn be IID samples from a Uniform(θ1, θ2) distribution. Derive method of moments estimators for both θ1 and θ2.
Let Y1, ..., Yn be IID samples from a Uniform(θ1, θ2) distribution. Derive method of moments...
2 Method of moments estimator for the uniform distribution Let Y1....,Y, be IID samples from a Uniform(0.02) distribution. Derive method of moments estimators for both ®, and 6
Please answer simply, clearly, and succinctly, and box/circle
the correct answer; thank you!
2 Method of moments estimator for the uniform distribution Let Y1, ..., Y, be IID samples from a Uniform(01.02) distribution. Derive method of moments estimators for both , and 82.
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.
QUESTION 6 Let Y., Y. , Yn denote a random sample of size n from a population whose density is given by , Yn) and θ2 = Ỹ. Two estimators for θ are θ,-nY(1) where Y(1)-min (h, ½, (a) Show that θ1 and θ2 are both unbiased estimators of θ (b) Find the efficiency ofa relative to θ2.
QUESTION 6 Let Y., Y. , Yn denote a random sample of size n from a population whose density is given by , Yn) and θ2 = Ỹ. Two estimators for θ are θ,-nY(1) where Y(1)-min (h, ½, (a) Show that θ1 and θ2 are both unbiased estimators of θ (b) Find the efficiency ofa relative to θ2.
Let X1, ...., Xm be iid N(μ1,σ2) and Y1, ..., Yn be iid N(μ2,σ2), and X's and Y's are independent. Here -∞<μ1,μ2<∞ and 0<σ<∞ are unknown. Derive the MLE for (μ1,μ2,σ2). Is the MLE sufficient for (μ1,μ2,σ2)? Also derive the MLE for (μ1-μ2)/σ.
Suppose that Y1,Y2,··· ,Yn is an iid from Y ∼ U(0,3). Find the limiting distribution of ¯ Y . What is the probability of average of Y from a random sample of 10 that exceed 1.6?
Let Y1, Y2, ..., Yn be independent random variables
each having uniform distribution on the interval (0, θ)
(c) Find var(Y(j) − Y(i)).
Let Y İ, Y2, , Yn be independent random variables each having uniform distribu- tion on the interval (0,0) Let Y İ, Y2, , Yn be independent random variables each having uniform distribu- tion on the interval (0,0)
(4) Let Yi, . .. ,y, be Ņ(θ, 1). Let θ,-yn and θ2-7. (a) What are the possible values of the θ (b) Find the bias and MSE of both the estimators. (c) Is one of the estimators better than the other? (d) For what values of θ is better than θ2?
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.