Answers: Probability Theory Prerequisite Review

Integration Review

  1.   $\frac{1}{2}$
  2.   $1$
  3.   $2\pi$
  4.   0

Evaluating Summations Review

  1.   $\frac{9}{2}$
  2.   $\frac{1}{162}$
  3.   $xe^{x^2}$
  4.   $10(1+x^2)^9$

Combinatorics Review

  1. (a) $324$ different orders

    (b) $306$ different orders

    (c) $108$ different orders

  1. (a) $4,845$

    (b) $116,280$

    (c) $1,980$

Set Operations Review

  1.   $A\cup B$
  2.   $A \cap B^C$, or $A \cup (A\cap B^C)$
  3.   $(A \cap B^C) \cup (B \cap A^C)$, or $[(S \cap [A\cup B]^C) \cup (A \cap B)]^C$
  4.   $[(A \cap B^C) \cup (B \cap A^C)]^C$, or $(S \cap [A\cup B]^C) \cup (A \cap B)$