Mathematics and Statistics Flashcards
6 cards from real EIT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Mathematics and Statistics flashcards as text
What is ∫(2x + 5)dx?
Answer: x² + 5x + C
Integrating term by term: ∫2x dx = x² and ∫5 dx = 5x, giving x² + 5x + C.
The eigenvalues of the matrix [[3,1],[0,2]] are:
Answer: 3 and 2
For an upper triangular matrix, eigenvalues are the diagonal entries: 3 and 2.
What does the Central Limit Theorem state?
Answer: The sample mean approaches a normal distribution as sample size increases
The Central Limit Theorem states that sample means approach a normal distribution as sample size grows, regardless of the population distribution.
What is the Taylor series expansion of e^x about x=0?
Answer: 1 + x + x²/2 + x³/6 + ...
The Taylor series of e^x = Σ(xⁿ/n!) = 1 + x + x²/2! + x³/3! + ...
If two random variables X and Y have a correlation coefficient of 0, they are:
Answer: Uncorrelated (but not necessarily independent)
A correlation of 0 means no linear relationship exists, but the variables could still have nonlinear dependence.
The gradient of a scalar function f(x,y) = x² + y² is:
Answer: (2x, 2y)
The gradient ∇f = (∂f/∂x, ∂f/∂y) = (2x, 2y) is a vector pointing in the direction of steepest ascent.