Let the five numbers 2, 3, 5, 9, 10 come from the uniform distribution on [a,b]....

Let the five numbers 2, 3, 5, 9, 10 come from the uniform distribution on [a,b]. Find the method of moments estimates of a and b.

Expert Solution

orchestra answered 1 year ago

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

2. Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]....

2. Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

2. Let X1, ..., Xn be a random sample from a uniform distribution on the interval...

2. Let X1, ..., Xn be a random sample from a uniform distribution on the interval (0, θ) where θ > 0 is a parameter. The prior distribution of the parameter has the pdf f(t) = βαβ/t^(β−1) for α < t < ∞ and zero elsewhere, where α > 0, β > 0. Find the Bayes estimator for θ. Describe the usefulness and the importance of Bayesian estimation. We are assuming that theta = t, but we are unsure if...

Let X have a uniform distribution on the interval [A, B]. (a) Obtain an expression for...

Let X have a uniform distribution on the interval [A, B]. (a) Obtain an expression for the (100p)th percentile, x. x = (b) Compute E(X), V(X), and σX. E(X) = V(X) = σX = (c) For n, a positive integer, compute E(Xn). E(Xn) =

1- Write a function f(n,a,b) that generates n random numbers # from Uniform(a,b) distribution and returns...

1- Write a function f(n,a,b) that generates n random numbers # from Uniform(a,b) distribution and returns their minimum. # Execute the function with n=100, a=1, b=9. 2- Replicate the function call f(100,1,9) 100 thousand times # and plot the empirical density of the minimum of 100 indep. Unif(1,9)'s 3-Use the sampling distribution from (b) to find 95% confidence # interval for the minimum of 100 independent Unif(1,9)'s. Please solve in R

Let X1, . . . , Xn be a random sample from a uniform distribution on...

Let X1, . . . , Xn be a random sample from a uniform distribution on the interval [a, b] (i) Find the moments estimators of a and b. (ii) Find the MLEs of a and b.

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform...

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform distribution on [-2,2]. a) what are the p.d.f.s of X and Y resp.? b) compute the means of X, Y. Can you use symmetry? c) compute the variance. Which variance is higher?

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11,...

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11, 11) for which the line tangent to the graph of f is parallel to the line joining (−11, f (−11)) and (11, f(11)). How many such numbers exist in the given interval? . 0 . 1 . 2 (correct) . 3 Enter points in increasing order (smallest first). Enter DNE in any empty answer blank. c = c = c = DNE (correct) 10....

Let X1,X2, . . . , Xn be a random sample from the uniform distribution with...

Let X1,X2, . . . , Xn be a random sample from the uniform distribution with pdf f(x; θ1, θ2) = 1/(2θ2), θ1 − θ2 < x < θ1 + θ2, where −∞ < θ1 < ∞ and θ2 > 0, and the pdf is equal to zero elsewhere. (a) Show that Y1 = min(Xi) and Yn = max(Xi), the joint sufficient statistics for θ1 and θ2, are complete. (b) Find the MVUEs of θ1 and θ2.

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on...

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on the interval (θ - 2, θ). a) Show that Ȳ is a biased estimator of θ. Calculate the bias. b) Calculate MSE( Ȳ). c) Find an unbiased estimator of θ. d) What is the mean square error of your unbiased estimator? e) Is your unbiased estimator a consistent estimator of θ?

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