HW 10-1 (Due Nov. 22, 2016) Name:
Print then work on it directly. Staple HW 10-1 and 10-2 together.
Problem 1
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Ehn
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.
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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).
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