STAT 401A prerequisites

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This page is intended to provide a summary of the mathematics, probability, and statistics background that you are expected to know before you take STAT 401A. Alternatively, you could find the relevant material in an introductory statistics textbook. Here are a few free options:

Exponents

For real numbers a,b, and c.

\( c^a c^b = c^{a+b} \)
\( (c^a)^b = c^{ab} \)
\( c^{-a} = 1/c^a \)
\( a^c b^c = (ab)^c \)
\( a^0 = 1 \)

Logarithms

For real numbers a, b, and c. \( \log \) refers to the natural logarithm, i.e. the log base \( e \), but the results here are true for any base.

\( \log(ab) = \log(a) + \log(b) \)
\( \log(a/b) = \log(a) - \log(b) \)
\( \log(a^c) = c \log(a) \)
\( \log(1) = 0 \)
\( \log(0) \) is undefined, i.e. it is negative infinity

Probability

Set theory

For sets A, B, and C in the sample space \( \Omega \) and an element \( \omega \) in \( \Omega \).

Intersection: \( P(A and B) = P(A \cap B) = { \omega : \omega \in A and \omega \in B} \)
Sets \( A \) and \( B \) are disjoint if there are no elements in \( A \) that are also in \( B \).

Axioms of probability (properties that are self-evident)

\( 0 \le P(A) \le 1 \)
\( P(\Omega) = 1 \)
If \( A \) and \( B \) are disjoint, then \( P(A or B) = P(A) + P(B). \)

Probability theory

Conditional probability \( P(A B) = P(A \cap B) / P(B) \) if \( P(B) > 0 \).