Probability

Question 1

Conditional Probability

Answer 1

Probability that something occurs given something else has already occured.

P[F l E] = P[F n E] / P[E]

Question 2

How to check if 2 events are independent

Answer 2

P(A n B) = P(A)*P(B)

Question 3

Mutually Exclusive Events

Answer 3

P(A n B) = 0

Question 4

Probability Mass Function [PMF]

Answer 4

Used for discrete variables.

ΣpX(x) = 1

Question 5

Probability Density Function [PDF]

Answer 5

Used for continuous variables.

P[a ≤ x ≤ b] = ∫[b,a]f(y) dy

To be a PDF it must satisfy:
∫[∞,-∞]f(y) dy = 1 & f(y) >0 for all y.

Question 6

Expectation of a random variable X

Answer 6

Discrete:
E[X] = Σxp(x)

Continuous:
E[X] = ∫[∞,-∞]xf(x) dx = 1

Question 7

Variance of a random variable X

Answer 7

V[X] = [(X - E[X])²]

V[X] = E[X²] - E[X]²