Question

[8] Let Y1<Y2<...<Yn be the order statistics of n independent observations from U(0, 1). (i) Find...

[8] Let Y1<Y2<...<Yn be the order statistics of n independent observations from U(0, 1).

(i) Find the p.d.f. of the r-th order statistics Yr.

(ii) Find the mean and variance of Yr.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Let Y1 < Y2 < · · · Ym be the order statistics of m...
1. Let Y1 < Y2 < · · · Ym be the order statistics of m independent observations X1, · · · , Xm from a uniform distribution on the interval [θ, θ + 1]. (a) (5 points) Find the distribution of Yr, where r is a integer and 1 ≤ r ≤ m. (b) (5 points) Calculate V ar(Ym) if θ = 0. (c) (5 points) Suppose θ is unknown, m = 5 and we have observed that x1...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution...
Let Y1,Y2,...,Yn denote a random sample of size n from a population with a uniform distribution on the interval (0,θ). Let Y(n)= max(Y1,Y2,...,Yn) and U = (1/θ)Y(n) . a) Show that U has cumulative density function 0 ,u<0, Fu (u) =   un ,0≤u≤1, 1 ,u>1
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].,Y(n)=max(Y1,Y2,....,Yn),which is considered as an estimator...
Let Y1,Y2.....,Yn be independent ,uniformly distributed random variables on the interval[0,θ].,Y(n)=max(Y1,Y2,....,Yn),which is considered as an estimator of θ. Explain why Y is a good estimator for θ when sample size is large.
Point Estimation by M.L.E. and Assessment by M.S.E.) Let Y1, · · · , Yn be...
Point Estimation by M.L.E. and Assessment by M.S.E.) Let Y1, · · · , Yn be a random sample from the p.d.f f(y | θ) = (r/θ)yr-1exp(−yr/θ), θ > 0, y > 0, where r is a known positive constant. (1) Find the M.L.E. of θ; (2) Find the M.S.E. of (estimator)θMLE.
Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ...
Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ > 0. (a) Find the MOM estimator for θ. (b) Find the ML estimator θˆ of θ. (c) Find the ML estimator τˆ of τ = P(Y1 ≤ a), for a ∈ (0,1). (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1−α CI for θ.
A binomial experiment consisting of n trials resulted in observations y1, y2,..., yn, where yi =...
A binomial experiment consisting of n trials resulted in observations y1, y2,..., yn, where yi = 1 if the ith trial was a success and yi = 0 otherwise. Find the MLE (MaximumLikelihood Estimator) of p, the probability of a success.
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean...
Let Y1, Y2, Y3 ,..,, Yn be a random sample from a normal distribution with mean µ and standard deviation 1. Then find the MVUE( Minimum - Variance Unbiased Estimation) for the parameters: µ^2 and µ(µ+1)
Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample...
Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 5 (Y1 < Y2 < Y3 < Y4 <Y5). from the distribution having pdf f(x) = e−x, 0 < x < ∞, zero elsewhere. Find P(Y5 ≥ 3).
5. Let Y1, Y2, ...Yn (independent and identically distributed. ∼ f(y; α) = 1/6 α8y3 ·...
5. Let Y1, Y2, ...Yn (independent and identically distributed. ∼ f(y; α) = 1/6 α8y3 · e^(−α2y3 ), 0 ≤ y < ∞, 0 < α < ∞. (a) (8 points) Find an expression for the Method of Moments estimator of α, ˜α. Show all work. (b) (8 points) Find an expression for the Maximum Likelihood estimator for α, ˆα. Show all work.
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 - λ, θ + λ) where -∞ < θ < ∞ and λ > 0. Find the method of moments estimators of θ and λ.