Posted by **Sean** on Thursday, October 8, 2009 at 5:51pm.

Joint probability density function is: x + y where 0<x<1 and 0<y<1 (0 elsewhere)

Find variance of (30x + 25y)

Answer is 11.48

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My calculations

Marginal probability density functions (same for x and y):

f(x) = x + 1/2 over 0<x<1

f(y) = y + 1/2 over 0<y<1

E(x) = E(y) = 7/12

E(x^2) = E(y^2) = 5/12

Var(x) = Var(y) = 11/144

E(x*y) = 1/3

Cov(x,y) = E(x*y) - E(x)*E(y) = -1/144

Var(30x + 25y) = 30^2 * Var(x) + 25^2 * Var(y) + 2 * 30 * 25 * Cov(x,y)

= 30^2 * 11/144 + 25^2 * 11/144 - 2 * 30 * 25 * 1/144

= 106.08

Where did I go wrong? Thanks!

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