View source for Example finding covariance of coin flips, Lec 10/15 ECE302Fall2008sanghavi - Rhea

[[Category:ECE302Fall2008_ProfSanghavi]]
[[Category:probabilities]]
[[Category:ECE302]]
[[Category:problem solving]]
=Question=
n coin flips, X = # of heads, Y = # of tails

Cov(X,Y) = ?

=Answer+
X + Y = n

E[X]+E[y] = n


Therefore:

X-E[X] + y-E[Y] = 0

X-E[X]= -(y-E[Y])

<math>Cov(X,Y)=-E[[X-E[X_ECE302Fall2008sanghavi]]^2]=-Var(X)=-Var(Y)</math>

and also the correlation coefficient is <math>\rho(X,Y)=-1</math>
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