For , let be the order statistics of independent draws from . (1) Find the PDF...

Question

Question

For $nin mathbb{N}$ , let $W_{1}<W_{2}<cdots <W_{2n+1}$ be the order statistics of $(2n+1$ independent draws from $Unif -1,1$ .

(1) Find the PDF of $Y_{2}$ .

(2) Compute $P[Y_{9}<1]$ .

Answer 1

Answer #1

f(w) w+I -1 B C2, 2n) 2 14Y, 그 2n_8 2 2 В 09, 2-?) 2h-8 ;-ㄧㄑㄌㄑㄧ The cd 8 (1+ys ) (1-%) dg 9-1 (23)

Answer 2

Similar Homework Help Questions

are order statistics from same distribution . Sample size is 3. Define and Finding marginal density...

are order statistics from same distribution . Sample size is 3. Define and Finding marginal density of . We were unable to transcribe this imageplz) = 1 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
are order statistics from same distribution . Sample size is 3. Define and Finding joint density...

are order statistics from same distribution . Sample size is 3. Define and Finding joint density of and . We were unable to transcribe this imageplz) = 1 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let and be two Gaussian random variables. (1) Sketch the PDFs of , on the same...

Let and be two Gaussian random variables. (1) Sketch the PDFs of , on the same chart. (2) Assuming , are independent, compute . X1N(4.2,1) X2~ N(12,70 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

(6) . We pick samples randomly from the population which distributes uniformly between the interval of. ....

(6) . We pick samples randomly from the population which distributes uniformly between the interval of. . Answer the following questions regarding the median of the samples Show that the distribution which follows has the distribution as shown below. Find the expected value of . Show = . When , show that is the consistent estimator of . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagen = 2m...
0Let X1, ....., Xn be iid Random variable from a Uniform distribution with pdf given by...

0Let X1, ....., Xn be iid Random variable from a Uniform distribution with pdf given by . (1) Is the 2-dimensional statistics T1(X) = (X(1), X(n)) a complete sufficient statistics? Justify your answer (2) Is the one-dimensional statistic a complete sufficient statistic? Justify your answer We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
#4. Let , , and be a random sample from f. Find the UMVUE for We...

#4. Let , , and be a random sample from f. Find the UMVUE for We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

Let X and Y be independent random variables with . Assume that and . Demonstrate that...

Let X and Y be independent random variables with . Assume that and . Demonstrate that Cov(X,Y) = 0 We were unable to transcribe this imageWe were unable to transcribe this image400 OC
Doob’s Decomposition: Let be a submartingale relative to the filtration . Show that there is a...

Doob’s Decomposition: Let be a submartingale relative to the filtration . Show that there is a martingale and a predictable sequence such that for all and . (Xm)m>o We were unable to transcribe this image(Mm)m>o (Am)m20 We were unable to transcribe this imagem>0 We were unable to transcribe this image
I have found answers to part a and b and just really need help with part...

I have found answers to part a and b and just really need help with part c! and the extra if you have time. A= for part a then for part b, I have 5. Wave mechanics: (10 points) Suppose to have the following wave function (-oo 〈 x 〈 +00) r2 a for constants A and a a) Determine A, by normalize V(x). b) Use Ψ(x) to find the expectation values (a), (z2)), and σ,-V(z2,-(z c) Find the momentum...

STATISTICS. REGIONS OF CONFIDENCE Let be a simple random sample (n) of the density , Find...

STATISTICS. REGIONS OF CONFIDENCE Let be a simple random sample (n) of the density , Find the confidence interval of 95% for the variance of the population. Thank you for your explanations. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image