HW 10-1 (Due Nov. 22, 2016) Namepeople.stat.sc.edu/wang528/Stat 511/HW 10 hints.pdfHW 10-2 (Due Nov. 22, 2016) Name: Print then work on it directly. Staple HW 10-1 and 10-2 together.

HW 10-1 (Due Nov. 22, 2016) Name:

Print then work on it directly. Staple HW 10-1 and 10-2 together.

Problem 1

1

Ehn

Problem 2

2

:there;

Problem 3

3

Effeteness;I.

Problem 4

4

:kF¥¥f¥:{" F¥±a

t÷*:

Problem 5

Why?

5

Problem 6

6

£MYnptin¥gygh = Mihama

by independence

M¥92 'k )

fy.y.IT , ,Y .)± fy.ly , )fy ,

lb ),1>0.1 . > 0

⇐- ofexply Fdffexpl ' )

↳P(Yz< Y ,c2Y . )= f?Mtv,

,%)dy,dy .P(Yi<

242 )= f? fottfiy , ,y.|d1dT .

HW 10-2 (Due Nov. 22, 2016) Name:

Print then work on it directly. Staple HW 10-1 and 10-2 together.

Problem 1 Suppose that Y1 and Y2 are random variables (discrete or continuous). Prove the

following results:

(a) Cov(Y1, Y2) = Cov(Y2, Y1).

(b) Cov(Y1, Y1) = V (Y1)

(c) Cov(a+ bY1, c+ dY2) = bdCov(Y1, Y2), for any constants a, b, c, and d.

1

Problem 2 Check Example 5.17 on Page 127 of the lecture notes. Find E(U2) and V (U2). And

then compute Cov(U1, U2).

2

Problem 3

3

Problem 4

4

If.tn#Eii

Problem 5

5

Problem 6

6

Itkin