Methods formulas

Question 1

Conditional probability

Answer 1

Pr(𝐴) = Pr(𝐴∩𝐵)/Pr(𝐵)if Pr(𝐵)≠0

Question 2

Total law of probability

Answer 2

Pr(𝐴) = Pr(𝐴|𝐵)Pr(𝐵)+Pr(𝐴|𝐵′)Pr(𝐵′)

Question 3

Independent probability conditions

Answer 3

• Pr(𝐴|𝐵)=Pr(𝐴)
• Pr(𝐵|𝐴)=Pr(𝐵)
• Pr(𝐴∩𝐵)=Pr(𝐴)×Pr(𝐵)

Question 4

Properties of the expected value/meanE(X)

Answer 4

• E(𝑋+𝑌)=E(𝑋)+E(𝑌)
• E(𝑎𝑋+𝑏)=𝑎E(𝑋)+𝑏 (for 𝑎, 𝑏 constant)

Question 5

Variance (Var(X))

Answer 5

Var(𝑋)= E(𝑋^2)−[E(𝑋)]^2

• measure of the spread of the probability distribution about its mean or expected value 𝜇
• denoted by 𝜎^2

Question 6

Standard deviation (sd(X))

Answer 6

sd(𝑋) = √Var(𝑋

• denoted by 𝜎

Question 7

Variance for binomial random variables

Answer 7

If 𝑋 is a binomial random variable with parameters 𝑛
and 𝑝:

Var(𝑋)=𝑛𝑝(1−𝑝)
.

Question 8

Expected value for a binomial random variable

Answer 8

If 𝑋 is a binomial random variable with parameters 𝑛
and 𝑝, then:

E(𝑋)=𝑛𝑝
.