Tutorial 3:Discrete Random Variables 1 Yihan Zhang and Baoxiang Wang Spring 2017 1
Tutorial 3: Discrete Random Variables 1 Yihan Zhang and Baoxiang Wang Spring 2017 1
Discrete Random variable Random Variable X Sample Space 2 X Real Number Line A random variable is discrete if its range is finite or countably infinite. Each discrete random variable has an associated probability mass function(PMF). toss a coin Head Tail Probability 1 1 2 2 2
Discrete Random Variable • A random variable is discrete if its range is finite or countably infinite. • Each discrete random variable has an associated probability mass function (PMF). Sample Space Ω Random Variable 𝑋 𝑥 Real Number Line toss a coin Head Tail Probability 1 2 1 2 2
Example 1:Discrete random variables Experiment Random Variable Possible Values Making 100 sales call sales 0,1,,100 Inspect 70 radios defective 0,1,…,70 Answer 20 questions correct 0,1,,20 Count cars at toll cars arriving 0,1,21 between 11:00-1:00 3
Example 1: Discrete random variables Experiment Random Variable Possible Values Making 100 sales call # sales 0,1,…,100 Inspect 70 radios # defective 0,1,…,70 Answer 20 questions # correct 0,1,…,20 Count cars at toll between 11:00-1:00 # cars arriving 0,1,2,…… 3
Example 2:Soccer Game ·2 games this weekend 0.4 probability----not losing the first game 0.7 probability----not losing the second game equally likely to win or tie 。independent 2 points for a win,1 for a tie and 0 for a loss. Find the PMF of the number of points that the team earns in this weekend. 4
Example 2: Soccer Game • 2 games this weekend • 0.4 probability----not losing the first game • 0.7 probability----not losing the second game • equally likely to win or tie • independent • 2 points for a win, 1 for a tie and 0 for a loss. • Find the PMF of the number of points that the team earns in this weekend. 4
Example 2:Soccer Game X1 2 1 0 X2 P 0.2 0.2 0.6 2 0.35 0.07 0.07 0.21 1 0.35 0.07 0.07 0.21 0 0.3 0.06 0.06 0.18 X=X1+X2 4 3 2 1 0 P 0.07 0.140.34 0.27 0.18 5
Example 2: Soccer Game 𝑋1 2 1 0 𝑋2 P 0.2 0.2 0.6 2 0.35 0.07 0.07 0.21 1 0.35 0.07 0.07 0.21 0 0.3 0.06 0.06 0.18 𝑿 = 𝑿𝟏 + 𝑿𝟐 4 3 2 1 0 𝑃 0.07 0.14 0.34 0.27 0.18 5