# The Algebra of SummationNotation

what is answer of these two following Summation?

$$\left(\sum_{i=1}^{3}p_i\cdot x_i\right)^2=?,$$

$$\sum_{i=1}^{3}p_i\cdot x_i^2=?$$

i think the first one is:

$$\left(\sum_{i=1}^{3}p_i\cdot x_i\right)^2=\left(p_1x_1+p_2x_2+p_3x_3\right)^2$$

but i dont know the second one Remark it is about Probability theory

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$x_1^2y_1+x_2^2y_2+x_3^2y_3$ is the answer to your question!

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Do you mean $$\sum_{i=1}^{3}y_i\cdot x_i^2=y_1x_1^2+y_2x_2^2+y_3x_3^2$$ ? The first one is correct by the way.
$\sum_i^3 p_i\cdot x_i^2=p_i\cdot (x_1+x_2+x_3)^2=p_1(x_1+x_2+x_3)^2+p_2 (x_1+x_2+x_3)^2+p_3(x_1+x_2+x_3)^2$