EIT Mathematics and Statistics 2

Question 1

What is ∫(2x + 5)dx?

Accepted Answer

x² + 5x + C

Answer

Integrating term by term: ∫2x dx = x² and ∫5 dx = 5x, giving x² + 5x + C.

Question 2

The eigenvalues of the matrix [[3,1],[0,2]] are:

Accepted Answer

3 and 2

Answer

For an upper triangular matrix, eigenvalues are the diagonal entries: 3 and 2.

Question 3

What does the Central Limit Theorem state?

Accepted Answer

The sample mean approaches a normal distribution as sample size increases

Answer

The Central Limit Theorem states that sample means approach a normal distribution as sample size grows, regardless of the population distribution.

Question 4

What is the Taylor series expansion of e^x about x=0?

Accepted Answer

1 + x + x²/2 + x³/6 + ...

Answer

The Taylor series of e^x = Σ(xⁿ/n!) = 1 + x + x²/2! + x³/3! + ...

Question 5

If two random variables X and Y have a correlation coefficient of 0, they are:

Accepted Answer

Uncorrelated (but not necessarily independent)

Answer

A correlation of 0 means no linear relationship exists, but the variables could still have nonlinear dependence.

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