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Given E[x]=3, var[x]=9, Graph the line y=(x-1)(x-2)(x-3).

How does one graph such a thing?

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if y=f(x) is a probability function: ;1. try finding appropriate range i.e by integrating area below curve and equating to "1" ;2. you may try: E(X)=x{Integral}f(x) ;3. and E(X^2)=x^2{Integral}f(x) enabling variance calculations... you would get separate equations possibly solvable for x.

I think using the above information would give you conditions on where the function 'y' exists and you may have to draw the graph over that range.

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    how would you find the roots?2012-09-07
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The answer is that you can't if you want to place a scatter plot going through the lines. Knowing only the mean and variance of X is not enough to know its probability distribution unless say you assume it is Gaussian. But to plot the line means that you want to show how the the (x,y) pairs vary with respect to the three lines you mention. Of course you can plot y=x-1, y=x-2 and y=x-3. But that doesn't require knowing the distribution for X.