From 6.3-3. Let Yi < Y2 < < Yg be the order statistics of 9 independent...
From 6.3-3. Let Y1 < Y2 < . . . < Y9 be the order statistics of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2. (2) Compute P[Y9 < 1]. From 6.3-3. Let Yǐ < ½ < . . . < y) be the order statistis of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2 2) Compute PY,1
Let Y1 < Y2 < : : : < Y9 be the order statistics of 9 independent draws from an exponential distribution that has a mean of 2. (1) Find the PDF of Y2. (2) Compute P[Y9 < 1].
From 6.3-6. For n E N, let W < W<< W2nt be the order statistics of (2n 1) independent draws from Unifl-1 2ra-+1 (1) Find the PDF of W and W2n+1 (2) By symmetry or otherwise, compute EW+
6.62. Let Yi < Y2 < . . . < Y, be the order statistics of a random sample of size n from the distribution having p.df.f(x)-2x/g, 0<x <θ, zero elsewhere (a) If 0 < c < 1, show that Pr (c < Y,/θ < 1)-1-eM (b) If n=5 and if the observed value of Y, is 1.8, find a 99 percent confidence interval for 0.
Let Y1< Y2< Y3< Y4< Y5 be the order statistics of n=5 independent observations from the exponential distribution with mean= 1. determine P(Y1>1) and find the pdf of Y5
. Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size n from an exponential distribution with parameter θ = 1. (a) Find the pdf of Yr. (b) Find the pdf of U = e −Yr .
For , let be the order statistics of independent draws from . (1) Find the PDF of . (2) Compute . We were unable to transcribe this imageWe were unable to transcribe this image(2n+1 Unif -1,1 We were unable to transcribe this imageWe were unable to transcribe this image
4. I. Let Yǐ < ½ < ⅓ < Ya be the order statistics of a random sample of size n = 4 from a distribution with pdf f(x) 322, 0<< 1, zero elsewhere. (a) Find the joint pdf of Ys and Ya (b) Find the conditional pdf of Ys, given Y-y (c) Evaluate Evsl (d) Compute the probability that the smallest of the random sample exceeds the median of the distribution
7.46. Let Yi < Y2 Y, be the order statistics of a random sample of size 3 from the distribution with p.d.f. zero elsewhere. Find the Joint p.d.f. of Z.-,, Z,-, and Z,- YYY,. The corresponding transformation maps the space 12 Show that z, and z, are joint sufficient statistics for θ1 and θ2. 7.46. Let Yi
Let X1, ..., Xn be a random sample from a population with pdf f(x 1/8,0 < x < θ, zero elsewhere. Let Yi < < Y, be the order statistics. Show that Y/Yn and Yn are independent random variables