Biostatistics with R/Some Basic Probability Concepts

Formular with R

Formular Number	Name	Formular	Formular with R
3.2.1	Classical probability	$P(E)={\frac {m}{N}}$	Example
3.2.2	Relative frequency probability	$P(E)={\frac {m}{n}}$	Example
3.3.1–3.3.3	Properties of probability	$P(E_{i})\geq 0$ $P(E_{1})+P(E_{2})+\dots +P(E_{n})=0$ $P(E_{i}+E_{j})=P(E_{i})+P(E_{j})$	Example
3.4.1	Multiplication rule	$P(A\cap B)=P(A\|B)P(B)=P(A)P(B\|A)$	Example
3.4.2	Conditional probability	$P(A\|B)={\frac {P(A\cap B)}{P(B)}}$	Example
3.4.3	Addition rule	$P(A\cup B)=P(A)+P(B)-P(A\cap B)$	Example
3.4.4	Independent events	$P(A\cap B)=P(A)P(B)$	Example
3.4.5	Complementary events	$P({\overline {A}})=1-P(A)$	Example
3.4.6	Marginal probability	$P(A_{i})=\sum {P(A_{i}\cap B_{j})}$	Example
	Sensitivity of a screening test	$P(T\|D)={\frac {a}{(a+c)}}$	Example
	Specificity of a screening test	$P({\overline {T}}\|{\overline {D}})={\frac {d}{(b+d)}}$	Example
3.5.1	Predictive value positive of a screening test	$P(D\|T)={\frac {P(D\|T)P(D)}{P(T\|D)P(D)+P(T\|{\overline {D}})P({\overline {D}})}}$	Example
3.5.2	Predictive value negative of a screening test	$P({\overline {D}}\|{\overline {T}})={\frac {P({\overline {D}}\|{\overline {T}})P({\overline {D}})}{P({\overline {T}}\|{\overline {D}})P({\overline {D}})+P({\overline {T}}\|D)P(D)}}$	Example
Symbol Key	$D$ = disease $E$ = Event $m$ = the number of times an event E_i occurs $n$ = sample size or the total number of times a process occurs $n$ =Population size or the total number of mutually exclusive and equally likely events $P({\overline {A}})$ = a complementary event; the probability of an event A, not occurring $P(E_{i})$ =probability of some event E_i occurring $P(A\cap B)$ =an “intersection” or “and” statement; the probability of an event A and an event B occurring $P(A\cup B)$ =an “union” or “or” statement; the probability of an event A or an event B or both occurring $P(A\|B)$ =a conditional statement; the probability of an event A occurring given that an event B has already occurred $T$ =test results		Example