EIT Mathematics and Statistics 2

Question 1

What is ∫(2x + 5)dx?

Accepted Answer

x² + 5x + C

Answer

2x² + 5x + C

Answer

x² + 5 + C

Answer

2x + C

Question 2

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

Accepted Answer

3 and 2

Answer

1 and 2

Answer

3 and 1

Answer

2 and 4

Question 3

What does the Central Limit Theorem state?

Accepted Answer

The sample mean approaches a normal distribution as sample size increases

Answer

All distributions are normal

Answer

Variance decreases with sample size

Answer

The population must be normal for statistics to work

Question 4

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

Accepted Answer

1 + x + x²/2 + x³/6 + ...

Answer

1 + x + x² + x³ + ...

Answer

x + x²/2 + x³/6 + ...

Answer

1 - x + x²/2 - x³/6 + ...

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

Perfectly correlated

Answer

Perfectly anticorrelated

Answer

Identical

Question 6

The gradient of a scalar function f(x,y) = x² + y² is:

Accepted Answer

(2x, 2y)

Answer

2x + 2y

Answer

2xy

Answer

x² + y²