Question

Question 2: Summation operator (a) Express the following in summation notation: $x_3y_3^2 + x_4y_4^2$. (b) Show that $\sum_{i=1}^{n} (y_i - \bar{y}) = 0$. (c) Show that $\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^{n} x_i(y_i - \bar{y})$.

          Question 2: Summation operator
(a) Express the following in summation notation: $x_3y_3^2 + x_4y_4^2$.
(b) Show that $\sum_{i=1}^{n} (y_i - \bar{y}) = 0$.
(c) Show that $\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y}) = \sum_{i=1}^{n} x_i(y_i - \bar{y})$.

Question 2: Summation operator
(a) Express the following in summation notation: x3y3^2 + x4y4^2.
(b) Show that ∑i=1^n (yi - y̅) = 0.
(c) Show that ∑i=1^n (xi - x̅)(yi - y̅) = ∑i=1^n xi(yi - y̅).

Added by Felix L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Likhit Ganedi

Step 1

The Σ symbol represents the sum of a series of terms. In this case, we have a series of terms (yi - y) for i = 1 to n. When we sum up all the terms (yi - y) for i = 1 to n, we can rewrite it as: (y1 - y) + (y2 - y) + ... + (yn - y) Expanding this expression, we Show more…

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Question 2: Summation Operator (a) Express the following in summation notation: x^3y^3 + x^4y? (b) Show that Î£(yi - y) = 0 (c) Show that Î£(xi - x)yi - y) = Î£xyi - y)