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 variableDiscrete Random Variables

µ = Σ y*P(y)

σ^2 = Σ (y - µ)2 * P(y)

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))

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

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 variableDiscrete Random Variables

µ = Σ y*P(y)

σ^2 = Σ (y - µ)2 * P(y)

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))

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