1.2 Discrete Probability Distributions

  1. Let \(\Omega\) = {a, b, c} be a sample space. Let m(a) = 1/2, m(b) = 1/3, and m(c) = 1/6. Find the probabilities for all eight subsets of \(\Omega\)

P(\(\Omega\)) = 0

P({a}) =1/2

P({b}) =1/3

P({c}) =1/6

P({a, b}) = 5/6

P({b, c}) = 1/2

P({a, c}) = 2/3

P({a,b,c}) = 1

2 Give a possible sample space for each of the following experiments:

  1. An election decides between two candidates A and B.

\(\Omega\) ={A,B}

  1. A two-sided coin is tossed.

\(\Omega\) ={heads, tails} #Uniform distribution

  1. A student is asked for the month of the year and the day of the week on which her birthday falls.

\(\Omega\) = {Fri/June, Mon/Mar, Tue/Apr, …}

  1. A student is chosen at random from a class of ten students.

\(\Omega\) ={1,2,3,4,5,6,7,8,9,10} # uniform distribution

  1. You receive a grade in this course.

\(\Omega\) ={A,B,C,D}

3 For which of the cases in Exercise 2 would it be reasonable to assign the uniform distribution function?

d and b are reasonable to assign uniform distribution.