• A∪B = P(A) + P(B) - P(A∩B)

  • (A or B) = A∪B

  • (A and B) = A∩B

• P(B|A) = P(A∩B) / P(A)

• A∩B = P(B|A)P(A)

• Independent = P(A|B) = P(A) and/or P(B)

• The probability of any single value is always zero for a continuous random variable

• Discrete Random Variables

  • µ = Σ y*P(y)

  • σ^2 = Σ (y - µ)2 * P(y)

Binomial Distribution

• Conditions

  • Mutually exclusive

  • Independent outcomes

  • Probability is constant

• P(Y = y) = nCy * (p)^y (1 - P)^n-y

• µ = np

σ^2 = sqrt(np(1 - P))

Normal Distribution

• Z = (X - µ) / σ

  • SD(Z) = 1

  • If Z is positive: x lies z# of SD’s above µ

  • If Z is negative: x lies z# of SD’s below µ

• X = µ + Zσ

• Z = normal when µ = 0 and σ = 1

• Right tail probability, we can define the right tail proability as P(Z > z)

• Example: Find the value of z such that P(Z < z) = #

  • Look for the # within the table (not the axes)

  • The corresponding axes make up the z