-random variable is a variable that assigns a number to each outcome of an experiment. This is not to be confused with an algebraic variable.

-the probability distribution of a random variable is a listing of each possible outcome of a random variable together with that outcomes probability

-X: X1, X2, X3...

-P(X): P1,P2,P3...

example: toss a coin 3 times. Let X=the number of heads

-X:0,1,2,3

-P(X): 1/8,3/8,3/8,1/8 Example:

S = {0,1,2,3,4,5,6,7,8}

A = {2,3,6,7} B = {0,3,6,8} A and B = {3,6}

A or B = {0,2,3,6,7,8}

A^c and B = {0,8}

A^c or B^c = {0,1,2,4,5,7,8}

(A and B)^c = {0,1,2,4,5,7,8}

(A or B)^c = {1,4,5}

A and A^c = {ø} the sample space is the set of all possible outcomes, denoted S

example: toss a coin three times. The sample space is ... S={HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

-the size of S is denoted lSl.

-example: toss a die twice. The sample space is... S={(1,1), (1,2),...(1,6), (2,1), (2,2),...(2,6),...(6,6)}

example: pull two cards from a well-shuffled deck. How many elements are in the sample space? ;