Unit 2 Formula Sheet
Chapter 3
Classical (or Theoretical) Probability:
\(P(E)=\frac{ \text {Number of Outcomes in Event E} }{ \text {Total number of outcomes in the sample space }}\)
Empirical (or Statistical) Probability:
\(P(E)=\frac{ \text {Frequency of event E} }{ \text {Total frequency} }=\frac fn\)
Probability of a Complement:
\(P(E')=1-P(E)\)
Probability of occurrence of both events A and B:
\(P(A\; \text {and} \;B)=P(A)\cdot P(\left.B\right|A)\)
\(P(A\; \text {and} \;B)=P(A)\cdot P(B)\) if \(A\; \text {and} \;B\) are independent
Probability of occurrence of either A or B:
\(P(A \; \text {or} \; B)=P(A)\;+\;P(B)\;-\;P(A \; \text {and} \; B)\)
\(P(A\; \text {or} \;B)=P(A)\;+\;P(B)\) if A and B are mutually exclusive
Chapter 4
Mean of a Discrete Random Variable:
\(\mu=\Sigma x\;P(x)\)
Variance and Standard Deviation of a Discrete Random Variable:
Variance: \(\sigma^2=\Sigma\left(x-\mu\right)^2\;P(x)\)
Standard Deviation: \(\sigma=\sqrt{\sigma^2}=\sqrt{\Sigma\left(x-\mu\right)^2\;P(x)}\)
Expected Value:
\(E(x)=\mu=\Sigma x\;P(x)\)
Binomial Probability of x successes in n trials:
\(P(x)={}_nC_x\;p^xq^{n-x}=\frac{n!}{(n-x)!x!}p^xq^{n-x}\)
Population Parameters of a Binomial Distribution:
Mean: \(\mu=np\)
Variance: \(\sigma^2=npq\)
Standard Deviation: \(\sigma=\sqrt{npq}\)