Permutations
and Combinations
Permutations: nPm
Combinations: nCm
Whole numbers: n
Probability
Formulas
Events: A, B
Probabity: P
Random variable: X, Y, Z
Values of random variable: x,
y, z
Expected value of X: μ
Any positive real number: ε
Standard deviation: σ
Variance: σ2
Density functions: f(x), f(t)
• Probability of an Event
,
Where
m is the number of possible outcomes,
n is the total number of possible outcomes.
• Range of Probability Values
• Certain Event
P(A)
= 1
• Impossible Event
P(A) = 0
• Complement
• Independent Events
P(A/B) = P(A),
P(B/A) = P(B),
• Addition Rule for Independent
P(A
∪ B) = P(A) + P(B)
• Multiplication Rule for Independent Events
• General Addition Rule
P(A ∪ B) = P(A) + P(B)
– P(A ∩ B)
where
A ∪ B is the union
of events A and B,
A ∩ B is the intersection of events A
and B.
• Condition Probability
• P(A
∩ B) = P(B) · P(A/B) = P(A)
· P(B/A)
• Law of Total Probability
,where Bi is a sequence of
mutually exclusive events.
• Bayes’ Theorem
• Bayes’ Formula
where
Bi is a set of mutually exclusive events
(hypotheses),
A is the final event,
P(Bi) are the prior
probabilities,
P(Bi / A) are the posterior probabilities.
• Law of Large Numbers
where
Sn is the sum of random variablea,
n is the number of possible outcomes.
• Chebyshev Inequality
where V(X) is the variance of X.
Sumber
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