[R] Using R to Compute Covariance

[Robert Sherry]

I have the following data set:
x    y           p
1    1          1/2
2    2          1/4
3    9          1/4

In this case, p represents the probability of the values occurring. I
compute the covariance of x and y by hand and come up with a value of 41/16.
When computing the covariance, I am dividing by n (in this case 3) not n-1.

I now want to use R to find the covarinace. I understand that R will divided
by n-1 not n.  Here are the commands that I issued:

x = c(1,2,3)
y = c(1,2,9)
df =dataframe(x,y)
w1 = c(1/2,1/4,1/4)
cov.wt(df, wt = w1 )

The last command returns:

$cov
     x    y
x 1.1  4.1
y 4.1 17.9

$center
    x    y
1.75 3.25

$n.obs
[1] 3

$wt
[1] 0.50 0.25 0.25

Therefore, I conclude that R is finding the covariance of x and y to be 4.1.
However, I need to adjust that number by multiplying it by 2 and then
dividing by 3. However, when I get that I still do not get 41/16.  What am I
missing?

I thank the group in advance for their responses.

Bob