JNU 2018 (SSS) Q.NO 11

Given,

y = 2w+4u

var(w) = 5

cov(w,u) = 1

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To find, cov(y,w) = E(yw) - E(y)E(w)

i.e, cov(y,w) = 2E(w^2) + 4E(uw) - [E(2w+4u)E(w)]

= 2E(w^2) + 4E(uw) - [2E(w)^2+4E(u)E(w)]

= 2E(w^2) + 4E(uw) - 2E(w)^2-4E(u)E(w)

= 2[E(w^2 - E(w)^2)] + 4[E(uw) - E(u)E(w)]

= 2var(w) + 4cov(w,u)

= (2 × 5) + (4 × 1)

= 10 + 4 = 14