Question

Consider $x_{1},x_{2},...,x_{n}$ observations such that $\sum_{i=1}^{n}{x_{i}}^{2}=500$ and $\sum_{i=1}^{n}x_{i}=50$. Then a minimum number of observations required is

• A. 25
• B. 5
• C. 10
• D. 15

Hint:

The Cauchy-Schwarz inequality for a vector of 1s and the vector $x$ provides the same result: $(\sum x_i)^2 \le n (\sum x_i^2)$. Plugging in the numbers: $2500 \le n(500) \implies n \ge 5$. It's a faster way to remember the relationship.

Answer 1

The Correct Option is B