The given image shows the summation notation:

$\sum_{i=1}^{13} 4Y_i$

To expand this sigma notation, we sum the expression $4Y_i$ as $i$ runs from 1 to 13:

$4Y_1 + 4Y_2 + 4Y_3 + \cdots + 4Y_{13}$

This is the expanded form of the given summation.

Would you like to delve deeper into this, or do you have any other questions?

Here are some related questions to further your understanding:

1. What is the general formula for the sum of a constant multiplied by a function over an index?
2. How would the expansion change if the upper limit of the summation was increased to 20?
3. What is the significance of the index $i$ in summation notation?
4. How can summation notation be applied to solve problems in statistics?
5. What are the properties of summation that make it a powerful tool in mathematics?

Tip: When expanding sigma notation, always ensure that each term corresponds to the correct value of the index to avoid mistakes.