Biostatistics, Chapter III & IV Notes

• 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

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