`Suppose that $(X, Y )$ has a uniform distribution on the parallelogram with vertices at
- $(0,0)$
- $(1292,1000)$
- $(1526,0)$
- $(2818,1000)$
Calculate the means of $X$ and of $Y$.
I don't know the formula for expectations of $X$ and $Y$.
2026-03-24 23:43:13.1774395793
Formula for expectation of Bivariate Data
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In the case of this particular question, the means of $X$ and $Y$ will be just the geometric center of the parallelogram as it is a uniform distribution.
Intuitive understanding
Think of the parallelogram as a dartboard, with one corner at the origin and its length on the X-axis. Think of the uniform distribution as a uniform force attracting darts, all across the parallelogram. Just consider the X-axis. When you throw darts at this parallelogram, since the force is uniform across X-axis, the mean of the darts will be the mean of length along the X-axis. A similar logic shows that the mean along Y-axis will be the mean of the height.