To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.
Describe a bivariate relationship's linearity, strength, and direction. In other words, plotting things that take two variables into consideration and trying to see whether there's a pattern with how they relate.
This is a brief conditional probability examplediscussing probabilities like P(A | B) using breakfast and lunch as examples.
This video talka about what is easily one of the most fundamental and profound concepts in statistics and maybe in all of mathematics. And that's the central limit theorem.
Understanding alternate coordinate systems. Created by Sal Khan.
Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).
Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.
Sociology often looks at different age cohorts. A cohort is simply a group of people, but here we're looking specifically at different age groups or generations, because these people all lived through the same certain events through a certain time that affected their lives similarly.
Dimension of the Column Space or Rank. Created by Sal Khan.
Dimension of the Null Space or Nullity. Created by Sal Khan.
This video defines the differences between discrete and continuous random variables, then works through examples of each.
Where we live in society plays a huge role in the environmental benefits and risks that we're exposed to.
Compare distributions using the features of shape, center, spread, and outliers.
Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.
Short video which describes the difference between a sample and a population.
Sal shows examples of intersection and union of sets and introduces some set notation.
We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might be wondering, is there the equivalent of matrix division? And before we get into that, let me introduce some concepts to you. And then we'll see that there is something that maybe isn't exactly division, but it's analogous to it.
Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Created by Sal Khan.
This 10-minute video lesson looks at Determinants: Finding the determinant of a 3x3 matrix.
This 22-minute video lesson shows another example of a projection matrix. It shows how to figure out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.