Probability Flashcards
1
Q
Conditional Probability
A
Probability that something occurs given something else has already occured.
P[F l E] = P[F n E] / P[E]
2
Q
How to check if 2 events are independent
A
P(A n B) = P(A)*P(B)
3
Q
Mutually Exclusive Events
A
P(A n B) = 0
4
Q
Probability Mass Function [PMF]
A
Used for discrete variables.
ΣpX(x) = 1
5
Q
Probability Density Function [PDF]
A
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.
6
Q
Expectation of a random variable X
A
Discrete:
E[X] = Σxp(x)
Continuous:
E[X] = ∫[∞,-∞]xf(x) dx = 1
7
Q
Variance of a random variable X
A
V[X] = [(X - E[X])²]
V[X] = E[X²] - E[X]²
