F2 Mathematical Foundations / Probability Theory I

Question 1

What is the formula for the variance of x

Answer 1

Var(x)=E[(x-my_x )^2]

Question 2

What is the formula for the mean of x

Answer 2

E(x)=(∑x_i )/n

Question 3

What are three types of probability theory?

Answer 3

1) Classical / frequentist
2) Empirical / bayesian
3) Subjective

Question 4

What is the difference between probabilistic and deterministic theories?

Answer 4

Probabilistic: If A then B is likely (used in political science)

Deterministic: If A then B.

Question 5

What is a distribution?

Answer 5

A set of values that a random variable may take. Each values has a weight (=probability)

Question 6

Which of the following a linear operator?
- Variance
- Expected value
- Integral

Answer 6

• Variance (no)
• Expected value (yes)
• Integral (yes)

Question 7

What is a constraint for the CDF?

Answer 7

It is non-decreasing. If x increases then the probability will always increase or be the same.

Question 8

What is a constraint of the PDF?

Answer 8

It is no defined for negativ values
f(x)>0