(New page: n coin flips, X = # of heads, Y = # of tails Cov(X,Y) = ? 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]]^2]=-Var(X)=-Var(Y)</m...) |
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| + | =Question= | ||
n coin flips, X = # of heads, Y = # of tails | n coin flips, X = # of heads, Y = # of tails | ||
Cov(X,Y) = ? | Cov(X,Y) = ? | ||
| − | + | =Answer+ | |
X + Y = n | X + Y = n | ||
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and also the correlation coefficient is <math>\rho(X,Y)=-1</math> | and also the correlation coefficient is <math>\rho(X,Y)=-1</math> | ||
| + | ---- | ||
| + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
Latest revision as of 13:29, 22 November 2011
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])
$ Cov(X,Y)=-E[[X-E[X_ECE302Fall2008sanghavi]]^2]=-Var(X)=-Var(Y) $
and also the correlation coefficient is $ \rho(X,Y)=-1 $
